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3 rectangular coordinate system

The document describes the rectangular coordinate system. It defines the system as using a grid with two perpendicular axes (x and y) that intersect at the origin (0,0). Any point in the plane can be located using its coordinates (x,y), where x is the distance from the y-axis and y is the distance from the x-axis. The four quadrants (I, II, III, IV) are defined by the intersection of the positive and negative sides of the x and y axes. Examples are given of labeling points and finding coordinates on the grid.

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Rectangular Coordinate System
A coordinate system is a system of assigning addresses for positions in the plane (2 D) or in space (3 D). Rectangular Coordinate System
A coordinate system is a system of assigning addresses for positions in the plane (2 D) or in space (3 D). The rectangular coordinate system for the plane consists of a rectangular grid where each point in the plane is addressed by an ordered pair of numbers (x, y). Rectangular Coordinate System
A coordinate system is a system of assigning addresses for positions in the plane (2 D) or in space (3 D). The rectangular coordinate system for the plane consists of a rectangular grid where each point in the plane is addressed by an ordered pair of numbers (x, y). Rectangular Coordinate System
A coordinate system is a system of assigning addresses for positions in the plane (2 D) or in space (3 D). The rectangular coordinate system for the plane consists of a rectangular grid where each point in the plane is addressed by an ordered pair of numbers (x, y). Rectangular Coordinate System The horizontal axis is called the x-axis.
A coordinate system is a system of assigning addresses for positions in the plane (2 D) or in space (3 D). The rectangular coordinate system for the plane consists of a rectangular grid where each point in the plane is addressed by an ordered pair of numbers (x, y). Rectangular Coordinate System The horizontal axis is called the x-axis. The vertical axis is called the y-axis.
A coordinate system is a system of assigning addresses for positions in the plane (2 D) or in space (3 D). The rectangular coordinate system for the plane consists of a rectangular grid where each point in the plane is addressed by an ordered pair of numbers (x, y). Rectangular Coordinate System The horizontal axis is called the x-axis. The vertical axis is called the y-axis. The point where the axes meet is called the origin.
A coordinate system is a system of assigning addresses for positions in the plane (2 D) or in space (3 D). The rectangular coordinate system for the plane consists of a rectangular grid where each point in the plane is addressed by an ordered pair of numbers (x, y). Rectangular Coordinate System The horizontal axis is called the x-axis. The vertical axis is called the y-axis. The point where the axes meet is called the origin. Starting from the origin, each point is addressed by its ordered pair (x, y) where:
A coordinate system is a system of assigning addresses for positions in the plane (2 D) or in space (3 D). The rectangular coordinate system for the plane consists of a rectangular grid where each point in the plane is addressed by an ordered pair of numbers (x, y). Rectangular Coordinate System The horizontal axis is called the x-axis. The vertical axis is called the y-axis. The point where the axes meet is called the origin. Starting from the origin, each point is addressed by its ordered pair (x, y) where: x = amount to move right (+) or left (–).
A coordinate system is a system of assigning addresses for positions in the plane (2 D) or in space (3 D). The rectangular coordinate system for the plane consists of a rectangular grid where each point in the plane is addressed by an ordered pair of numbers (x, y). Rectangular Coordinate System The horizontal axis is called the x-axis. The vertical axis is called the y-axis. The point where the axes meet is called the origin. Starting from the origin, each point is addressed by its ordered pair (x, y) where: x = amount to move right (+) or left (–). y = amount to move up (+) or down (–).
x = amount to move right (+) or left (–). y = amount to move up (+) or down (–). Rectangular Coordinate System
x = amount to move right (+) or left (–). y = amount to move up (+) or down (–). For example, the point P corresponds to (4, –3) Rectangular Coordinate System
x = amount to move right (+) or left (–). y = amount to move up (+) or down (–). For example, the point P corresponds to (4, –3) is 4 right, Rectangular Coordinate System
x = amount to move right (+) or left (–). y = amount to move up (+) or down (–). For example, the point P corresponds to (4, –3) is 4 right, and 3 down from the origin. Rectangular Coordinate System (4, –3) P
x = amount to move right (+) or left (–). y = amount to move up (+) or down (–). For example, the point P corresponds to (4, –3) is 4 right, and 3 down from the origin. Rectangular Coordinate System Example A. Label the points A(-1, 2), B(-3, -2),C(0, -5).
x = amount to move right (+) or left (–). y = amount to move up (+) or down (–). For example, the point P corresponds to (4, –3) is 4 right, and 3 down from the origin. Rectangular Coordinate System Example A. Label the points A(-1, 2), B(-3, -2),C(0, -5). A
x = amount to move right (+) or left (–). y = amount to move up (+) or down (–). For example, the point P corresponds to (4, –3) is 4 right, and 3 down from the origin. Rectangular Coordinate System Example A. Label the points A(-1, 2), B(-3, -2),C(0, -5). A B
x = amount to move right (+) or left (–). y = amount to move up (+) or down (–). For example, the point P corresponds to (4, –3) is 4 right, and 3 down from the origin. Rectangular Coordinate System Example A. Label the points A(-1, 2), B(-3, -2),C(0, -5). A B C
x = amount to move right (+) or left (–). y = amount to move up (+) or down (–). For example, the point P corresponds to (4, –3) is 4 right, and 3 down from the origin. Rectangular Coordinate System Example A. Label the points A(-1, 2), B(-3, -2),C(0, -5). The ordered pair (x, y) corresponds to a point is called the coordinate of the point, x is the x-coordinate and y is the y-coordinate. A B C
x = amount to move right (+) or left (–). y = amount to move up (+) or down (–). For example, the point P corresponds to (4, –3) is 4 right, and 3 down from the origin. Rectangular Coordinate System Example A. Label the points A(-1, 2), B(-3, -2),C(0, -5). The ordered pair (x, y) corresponds to a point is called the coordinate of the point, x is the x-coordinate and y is the y-coordinate. A B C Example B: Find the coordinate of P, Q, R as shown. P Q R
x = amount to move right (+) or left (–). y = amount to move up (+) or down (–). For example, the point P corresponds to (4, –3) is 4 right, and 3 down from the origin. Rectangular Coordinate System Example A. Label the points A(-1, 2), B(-3, -2),C(0, -5). The ordered pair (x, y) corresponds to a point is called the coordinate of the point, x is the x-coordinate and y is the y-coordinate. A B C Example B: Find the coordinate of P, Q, R as shown. P(4, 5), P Q R
x = amount to move right (+) or left (–). y = amount to move up (+) or down (–). For example, the point P corresponds to (4, –3) is 4 right, and 3 down from the origin. Rectangular Coordinate System Example A. Label the points A(-1, 2), B(-3, -2),C(0, -5). The ordered pair (x, y) corresponds to a point is called the coordinate of the point, x is the x-coordinate and y is the y-coordinate. A B C Example B: Find the coordinate of P, Q, R as shown. P(4, 5), Q(3, -5), P Q R
x = amount to move right (+) or left (–). y = amount to move up (+) or down (–). For example, the point P corresponds to (4, –3) is 4 right, and 3 down from the origin. Rectangular Coordinate System Example A. Label the points A(-1, 2), B(-3, -2),C(0, -5). The ordered pair (x, y) corresponds to a point is called the coordinate of the point, x is the x-coordinate and y is the y-coordinate. A B C Example B: Find the coordinate of P, Q, R as shown. P(4, 5), Q(3, -5), R(-6, 0) P Q R
The coordinate of the origin is (0, 0). (0,0) Rectangular Coordinate System
The coordinate of the origin is (0, 0). Any point on the x-axis has coordinate of the form (x, 0). (0,0) Rectangular Coordinate System
The coordinate of the origin is (0, 0). Any point on the x-axis has coordinate of the form (x, 0). (5, 0) (0,0) Rectangular Coordinate System
The coordinate of the origin is (0, 0). Any point on the x-axis has coordinate of the form (x, 0). (5, 0)(-6, 0) (0,0) Rectangular Coordinate System
The coordinate of the origin is (0, 0). Any point on the x-axis has coordinate of the form (x, 0). (5, 0)(-6, 0) Any point on the y-axis has coordinate of the form (0, y).(0,0) Rectangular Coordinate System
The coordinate of the origin is (0, 0). Any point on the x-axis has coordinate of the form (x, 0). (5, 0)(-6, 0) Any point on the y-axis has coordinate of the form (0, y). (0, 6) (0,0) Rectangular Coordinate System
The coordinate of the origin is (0, 0). Any point on the x-axis has coordinate of the form (x, 0). (5, 0)(-6, 0) Any point on the y-axis has coordinate of the form (0, y). (0, -4) (0, 6) (0,0) Rectangular Coordinate System
The coordinate of the origin is (0, 0). Any point on the x-axis has coordinate of the form (x, 0). Any point on the y-axis has coordinate of the form (0, y). Rectangular Coordinate System The axes divide the plane into four parts. Counter clockwise, they are denoted as quadrants I, II, III, and IV. QIQII QIII QIV
The coordinate of the origin is (0, 0). Any point on the x-axis has coordinate of the form (x, 0). Any point on the y-axis has coordinate of the form (0, y). Rectangular Coordinate System The axes divide the plane into four parts. Counter clockwise, they are denoted as quadrants I, II, III, and IV. QIQII QIII QIV (+,+)
The coordinate of the origin is (0, 0). Any point on the x-axis has coordinate of the form (x, 0). Any point on the y-axis has coordinate of the form (0, y). Rectangular Coordinate System The axes divide the plane into four parts. Counter clockwise, they are denoted as quadrants I, II, III, and IV. QIQII QIII QIV (+,+)(–,+)
The coordinate of the origin is (0, 0). Any point on the x-axis has coordinate of the form (x, 0). Any point on the y-axis has coordinate of the form (0, y). Rectangular Coordinate System Q1Q2 Q3 Q4 (+,+)(–,+) (–,–) (+,–) The axes divide the plane into four parts. Counter clockwise, they are denoted as quadrants I, II, III, and IV. Respectively, the signs of the coordinates of each quadrant are shown.
When the x-coordinate of the a point (x, y) is changed to its opposite as (–x , y), the new point is the reflection across the y-axis. (5,4) Rectangular Coordinate System
When the x-coordinate of the a point (x, y) is changed to its opposite as (–x , y), the new point is the reflection across the y-axis. (5,4)(–5,4) Rectangular Coordinate System
When the x-coordinate of the a point (x, y) is changed to its opposite as (–x , y), the new point is the reflection across the y-axis. When the y-coordinate of the a point (x, y) is changed to its opposite as (x , –y), the new point is the reflection across the x-axis. (5,4)(–5,4) Rectangular Coordinate System
When the x-coordinate of the a point (x, y) is changed to its opposite as (–x , y), the new point is the reflection across the y-axis. When the y-coordinate of the a point (x, y) is changed to its opposite as (x , –y), the new point is the reflection across the x-axis. (5,4)(–5,4) (5, –4) Rectangular Coordinate System
When the x-coordinate of the a point (x, y) is changed to its opposite as (–x , y), the new point is the reflection across the y-axis. When the y-coordinate of the a point (x, y) is changed to its opposite as (x , –y), the new point is the reflection across the x-axis. (5,4)(–5,4) (5, –4) (–x, –y) is the reflection of (x, y) across the origin. Rectangular Coordinate System
When the x-coordinate of the a point (x, y) is changed to its opposite as (–x , y), the new point is the reflection across the y-axis. When the y-coordinate of the a point (x, y) is changed to its opposite as (x , –y), the new point is the reflection across the x-axis. (5,4)(–5,4) (5, –4) (–x, –y) is the reflection of (x, y) across the origin. (–5, –4) Rectangular Coordinate System
Movements and Coordinates Rectangular Coordinate System
Movements and Coordinates Let A be the point (2, 3). Rectangular Coordinate System A (2, 3)
Movements and Coordinates Let A be the point (2, 3). Suppose it’s x–coordinate is increased by 4 to (2 + 4, 3) = (6, 3) Rectangular Coordinate System A (2, 3)
Movements and Coordinates Let A be the point (2, 3). Suppose it’s x–coordinate is increased by 4 to (2 + 4, 3) = (6, 3) - to the point B, Rectangular Coordinate System A B (2, 3) (6, 3)
Movements and Coordinates Let A be the point (2, 3). Suppose it’s x–coordinate is increased by 4 to (2 + 4, 3) = (6, 3) - to the point B, this corresponds to moving A to the right by 4. Rectangular Coordinate System A B x–coord. increased by 4 (2, 3) (6, 3)
Movements and Coordinates Let A be the point (2, 3). Suppose it’s x–coordinate is increased by 4 to (2 + 4, 3) = (6, 3) - to the point B, this corresponds to moving A to the right by 4. Rectangular Coordinate System A B Similarly if the x–coordinate of (2, 3) is decreased by 4 to (2 – 4, 3) = (–2, 3) x–coord. increased by 4 (2, 3) (6, 3)
Movements and Coordinates Let A be the point (2, 3). Suppose it’s x–coordinate is increased by 4 to (2 + 4, 3) = (6, 3) - to the point B, this corresponds to moving A to the right by 4. Rectangular Coordinate System A B Similarly if the x–coordinate of (2, 3) is decreased by 4 to (2 – 4, 3) = (–2, 3) - to the point C, C x–coord. increased by 4 x–coord. decreased by 4 (2, 3) (6, 3)(–2, 3)
Movements and Coordinates Let A be the point (2, 3). Suppose it’s x–coordinate is increased by 4 to (2 + 4, 3) = (6, 3) - to the point B, this corresponds to moving A to the right by 4. Rectangular Coordinate System A B Similarly if the x–coordinate of (2, 3) is decreased by 4 to (2 – 4, 3) = (–2, 3) - to the point C, this corresponds to moving A to the left by 4. C x–coord. increased by 4 x–coord. decreased by 4 (2, 3) (6, 3)(–2, 3)
Movements and Coordinates Let A be the point (2, 3). Suppose it’s x–coordinate is increased by 4 to (2 + 4, 3) = (6, 3) - to the point B, this corresponds to moving A to the right by 4. Rectangular Coordinate System A B Similarly if the x–coordinate of (2, 3) is decreased by 4 to (2 – 4, 3) = (–2, 3) - to the point C, this corresponds to moving A to the left by 4. Hence we conclude that changes in the x–coordinates of a point move the point right and left. C x–coord. increased by 4 x–coord. decreased by 4 (2, 3) (6, 3)(–2, 3)
Movements and Coordinates Let A be the point (2, 3). Suppose it’s x–coordinate is increased by 4 to (2 + 4, 3) = (6, 3) - to the point B, this corresponds to moving A to the right by 4. Rectangular Coordinate System A B Similarly if the x–coordinate of (2, 3) is decreased by 4 to (2 – 4, 3) = (–2, 3) - to the point C, this corresponds to moving A to the left by 4. Hence we conclude that changes in the x–coordinates of a point move the point right and left. If the x–change is +, the point moves to the right. C x–coord. increased by 4 x–coord. decreased by 4 (2, 3) (6, 3)(–2, 3)
Movements and Coordinates Let A be the point (2, 3). Suppose it’s x–coordinate is increased by 4 to (2 + 4, 3) = (6, 3) - to the point B, this corresponds to moving A to the right by 4. Rectangular Coordinate System A B Similarly if the x–coordinate of (2, 3) is decreased by 4 to (2 – 4, 3) = (–2, 3) - to the point C, this corresponds to moving A to the left by 4. Hence we conclude that changes in the x–coordinates of a point move the point right and left. If the x–change is +, the point moves to the right. If the x–change is – , the point moves to the left. C x–coord. increased by 4 x–coord. decreased by 4 (2, 3) (6, 3)(–2, 3)
Again let A be the point (2, 3). Rectangular Coordinate System A (2, 3)
Again let A be the point (2, 3). Suppose its y–coordinate is increased by 4 to (2, 3 + 4) = (2, 7) Rectangular Coordinate System A (2, 3)
Again let A be the point (2, 3). Suppose its y–coordinate is increased by 4 to (2, 3 + 4) = (2, 7) - to the point D, Rectangular Coordinate System A D y–coord. increased by 4 (2, 3) (2, 7)
Again let A be the point (2, 3). Suppose its y–coordinate is increased by 4 to (2, 3 + 4) = (2, 7) - to the point D, this corresponds to moving A up by 4. Rectangular Coordinate System A D y–coord. increased by 4 (2, 3) (2, 7)
Again let A be the point (2, 3). Suppose its y–coordinate is increased by 4 to (2, 3 + 4) = (2, 7) - to the point D, this corresponds to moving A up by 4. Rectangular Coordinate System A D Similarly if the y–coordinate of (2, 3) is decreased by 4 to (2, 3 – 4) = (2, –1) - to the point E, E y–coord. increased by 4 y–coord. decreased by 4 (2, 3) (2, 7) (2, –1)
Again let A be the point (2, 3). Suppose its y–coordinate is increased by 4 to (2, 3 + 4) = (2, 7) - to the point D, this corresponds to moving A up by 4. Rectangular Coordinate System A D Similarly if the y–coordinate of (2, 3) is decreased by 4 to (2, 3 – 4) = (2, –1) - to the point E, this corresponds to moving A down by 4. E y–coord. increased by 4 y–coord. decreased by 4 (2, 3) (2, 7) (2, –1)
Again let A be the point (2, 3). Suppose its y–coordinate is increased by 4 to (2, 3 + 4) = (2, 7) - to the point D, this corresponds to moving A up by 4. Rectangular Coordinate System A D Similarly if the y–coordinate of (2, 3) is decreased by 4 to (2, 3 – 4) = (2, –1) - to the point E, this corresponds to moving A down by 4. Hence we conclude that changes in the y–coordinates of a point move the point right and left. E y–coord. increased by 4 y–coord. decreased by 4 (2, 3) (2, 7) (2, –1)
Again let A be the point (2, 3). Suppose its y–coordinate is increased by 4 to (2, 3 + 4) = (2, 7) - to the point D, this corresponds to moving A up by 4. Rectangular Coordinate System A D Similarly if the y–coordinate of (2, 3) is decreased by 4 to (2, 3 – 4) = (2, –1) - to the point E, this corresponds to moving A down by 4. Hence we conclude that changes in the y–coordinates of a point move the point right and left. If the y–change is +, the point moves up. E y–coord. increased by 4 y–coord. decreased by 4 (2, 3) (2, 7) (2, –1)
Again let A be the point (2, 3). Suppose its y–coordinate is increased by 4 to (2, 3 + 4) = (2, 7) - to the point D, this corresponds to moving A up by 4. Rectangular Coordinate System A D Similarly if the y–coordinate of (2, 3) is decreased by 4 to (2, 3 – 4) = (2, –1) - to the point E, this corresponds to moving A down by 4. Hence we conclude that changes in the y–coordinates of a point move the point right and left. If the y–change is +, the point moves up. If the y–change is – , the point moves down. E y–coord. increased by 4 y–coord. decreased by 4 (2, 3) (2, 7) (2, –1)
Rectangular Coordinate System Example. C. a. Let A be the point (–2, 4). What is the coordinate of the point B that is 100 units directly left of A?
Rectangular Coordinate System Example. C. a. Let A be the point (–2, 4). What is the coordinate of the point B that is 100 units directly left of A? Moving left corresponds to decreasing the x-coordinate.
Rectangular Coordinate System Example. C. a. Let A be the point (–2, 4). What is the coordinate of the point B that is 100 units directly left of A? Moving left corresponds to decreasing the x-coordinate. Hence B is (–2 – 100, 4)
Rectangular Coordinate System Example. C. a. Let A be the point (–2, 4). What is the coordinate of the point B that is 100 units directly left of A? Moving left corresponds to decreasing the x-coordinate. Hence B is (–2 – 100, 4) = (–102, 4).
Rectangular Coordinate System Example. C. a. Let A be the point (–2, 4). What is the coordinate of the point B that is 100 units directly left of A? Moving left corresponds to decreasing the x-coordinate. Hence B is (–2 – 100, 4) = (–102, 4). b. What is the coordinate of the point C that is 100 units directly above A?
Rectangular Coordinate System Example. C. a. Let A be the point (–2, 4). What is the coordinate of the point B that is 100 units directly left of A? Moving left corresponds to decreasing the x-coordinate. Hence B is (–2 – 100, 4) = (–102, 4). b. What is the coordinate of the point C that is 100 units directly above A? Moving up corresponds to increasing the y-coordinate.
Rectangular Coordinate System Example. C. a. Let A be the point (–2, 4). What is the coordinate of the point B that is 100 units directly left of A? Moving left corresponds to decreasing the x-coordinate. Hence B is (–2 – 100, 4) = (–102, 4). b. What is the coordinate of the point C that is 100 units directly above A? Moving up corresponds to increasing the y-coordinate. Hence C is (–2, 4) = (–2, 4 +100)
Rectangular Coordinate System Example. C. a. Let A be the point (–2, 4). What is the coordinate of the point B that is 100 units directly left of A? Moving left corresponds to decreasing the x-coordinate. Hence B is (–2 – 100, 4) = (–102, 4). b. What is the coordinate of the point C that is 100 units directly above A? Moving up corresponds to increasing the y-coordinate. Hence C is (–2, 4) = (–2, 4 +100) = (–2, 104).
Rectangular Coordinate System Example. C. a. Let A be the point (–2, 4). What is the coordinate of the point B that is 100 units directly left of A? Moving left corresponds to decreasing the x-coordinate. Hence B is (–2 – 100, 4) = (–102, 4). b. What is the coordinate of the point C that is 100 units directly above A? Moving up corresponds to increasing the y-coordinate. Hence C is (–2, 4) = (–2, 4 +100) = (–2, 104). c. What is the coordinate of the point D that is 50 to the right and 30 below A?
Rectangular Coordinate System Example. C. a. Let A be the point (–2, 4). What is the coordinate of the point B that is 100 units directly left of A? Moving left corresponds to decreasing the x-coordinate. Hence B is (–2 – 100, 4) = (–102, 4). b. What is the coordinate of the point C that is 100 units directly above A? Moving up corresponds to increasing the y-coordinate. Hence C is (–2, 4) = (–2, 4 +100) = (–2, 104). c. What is the coordinate of the point D that is 50 to the right and 30 below A? We need to add 50 to the x–coordinate (to the right)
Rectangular Coordinate System Example. C. a. Let A be the point (–2, 4). What is the coordinate of the point B that is 100 units directly left of A? Moving left corresponds to decreasing the x-coordinate. Hence B is (–2 – 100, 4) = (–102, 4). b. What is the coordinate of the point C that is 100 units directly above A? Moving up corresponds to increasing the y-coordinate. Hence C is (–2, 4) = (–2, 4 +100) = (–2, 104). c. What is the coordinate of the point D that is 50 to the right and 30 below A? We need to add 50 to the x–coordinate (to the right) and subtract 30 from the y–coordinate (to go down).
Rectangular Coordinate System Example. C. a. Let A be the point (–2, 4). What is the coordinate of the point B that is 100 units directly left of A? Moving left corresponds to decreasing the x-coordinate. Hence B is (–2 – 100, 4) = (–102, 4). b. What is the coordinate of the point C that is 100 units directly above A? Moving up corresponds to increasing the y-coordinate. Hence C is (–2, 4) = (–2, 4 +100) = (–2, 104). c. What is the coordinate of the point D that is 50 to the right and 30 below A? We need to add 50 to the x–coordinate (to the right) and subtract 30 from the y–coordinate (to go down). Hence D has coordinate (–2 + 50, 4 – 30)
Rectangular Coordinate System Example. C. a. Let A be the point (–2, 4). What is the coordinate of the point B that is 100 units directly left of A? Moving left corresponds to decreasing the x-coordinate. Hence B is (–2 – 100, 4) = (–102, 4). b. What is the coordinate of the point C that is 100 units directly above A? Moving up corresponds to increasing the y-coordinate. Hence C is (–2, 4) = (–2, 4 +100) = (–2, 104). c. What is the coordinate of the point D that is 50 to the right and 30 below A? We need to add 50 to the x–coordinate (to the right) and subtract 30 from the y–coordinate (to go down). Hence D has coordinate (–2 + 50, 4 – 30) = (48, –26).
Exercise. A. a. Write down the coordinates of the following points. Rectangular Coordinate System AB C D E F G H
Ex. B. Plot the following points on the graph paper. Rectangular Coordinate System 2. a. (2, 0) b. (–2, 0) c. (5, 0) d. (–8, 0) e. (–10, 0) All these points are on which axis? 3. a. (0, 2) b. (0, –2) c. (0, 5) d. (0, –6) e. (0, 7) All these points are on which quadrant? 4. a. (5, 2) b. (2, 5) c. (1, 7) d. (7, 1) e. (6, 6) All these points are in which quadrant? 5. a. (–5, –2) b. (–2, –5) c. (–1, –7) d. (–7, –1) e. (–6, –6) All these points are in which quadrant? 6. List three coordinates whose locations are in the 2nd quadrant and plot them. 7. List three coordinates whose locations are in the 4th quadrant and plot them.
C. Find the coordinates of the following points. Draw both points for each problem. Rectangular Coordinate System The point that’s 8. 5 units to the right of (3, –2). 10. 4 units to the left of (–1, –5). 9. 6 units to the right of (–4, 2). 11. 6 units to the left of (2, –6). 12. 3 units to the left and 6 units down from (–2, 5). 13. 1 unit to the right and 5 units up from (–3, 1). 14. 3 units to the right and 3 units down from (–3, 4). 15. 2 units to the left and 6 units up from (4, –1).

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3 rectangular coordinate system

  • 1.
  • 2.
    A coordinate systemis a system of assigning addresses for positions in the plane (2 D) or in space (3 D). Rectangular Coordinate System
  • 3.
    A coordinate systemis a system of assigning addresses for positions in the plane (2 D) or in space (3 D). The rectangular coordinate system for the plane consists of a rectangular grid where each point in the plane is addressed by an ordered pair of numbers (x, y). Rectangular Coordinate System
  • 4.
    A coordinate systemis a system of assigning addresses for positions in the plane (2 D) or in space (3 D). The rectangular coordinate system for the plane consists of a rectangular grid where each point in the plane is addressed by an ordered pair of numbers (x, y). Rectangular Coordinate System
  • 5.
    A coordinate systemis a system of assigning addresses for positions in the plane (2 D) or in space (3 D). The rectangular coordinate system for the plane consists of a rectangular grid where each point in the plane is addressed by an ordered pair of numbers (x, y). Rectangular Coordinate System The horizontal axis is called the x-axis.
  • 6.
    A coordinate systemis a system of assigning addresses for positions in the plane (2 D) or in space (3 D). The rectangular coordinate system for the plane consists of a rectangular grid where each point in the plane is addressed by an ordered pair of numbers (x, y). Rectangular Coordinate System The horizontal axis is called the x-axis. The vertical axis is called the y-axis.
  • 7.
    A coordinate systemis a system of assigning addresses for positions in the plane (2 D) or in space (3 D). The rectangular coordinate system for the plane consists of a rectangular grid where each point in the plane is addressed by an ordered pair of numbers (x, y). Rectangular Coordinate System The horizontal axis is called the x-axis. The vertical axis is called the y-axis. The point where the axes meet is called the origin.
  • 8.
    A coordinate systemis a system of assigning addresses for positions in the plane (2 D) or in space (3 D). The rectangular coordinate system for the plane consists of a rectangular grid where each point in the plane is addressed by an ordered pair of numbers (x, y). Rectangular Coordinate System The horizontal axis is called the x-axis. The vertical axis is called the y-axis. The point where the axes meet is called the origin. Starting from the origin, each point is addressed by its ordered pair (x, y) where:
  • 9.
    A coordinate systemis a system of assigning addresses for positions in the plane (2 D) or in space (3 D). The rectangular coordinate system for the plane consists of a rectangular grid where each point in the plane is addressed by an ordered pair of numbers (x, y). Rectangular Coordinate System The horizontal axis is called the x-axis. The vertical axis is called the y-axis. The point where the axes meet is called the origin. Starting from the origin, each point is addressed by its ordered pair (x, y) where: x = amount to move right (+) or left (–).
  • 10.
    A coordinate systemis a system of assigning addresses for positions in the plane (2 D) or in space (3 D). The rectangular coordinate system for the plane consists of a rectangular grid where each point in the plane is addressed by an ordered pair of numbers (x, y). Rectangular Coordinate System The horizontal axis is called the x-axis. The vertical axis is called the y-axis. The point where the axes meet is called the origin. Starting from the origin, each point is addressed by its ordered pair (x, y) where: x = amount to move right (+) or left (–). y = amount to move up (+) or down (–).
  • 11.
    x = amountto move right (+) or left (–). y = amount to move up (+) or down (–). Rectangular Coordinate System
  • 12.
    x = amountto move right (+) or left (–). y = amount to move up (+) or down (–). For example, the point P corresponds to (4, –3) Rectangular Coordinate System
  • 13.
    x = amountto move right (+) or left (–). y = amount to move up (+) or down (–). For example, the point P corresponds to (4, –3) is 4 right, Rectangular Coordinate System
  • 14.
    x = amountto move right (+) or left (–). y = amount to move up (+) or down (–). For example, the point P corresponds to (4, –3) is 4 right, and 3 down from the origin. Rectangular Coordinate System (4, –3) P
  • 15.
    x = amountto move right (+) or left (–). y = amount to move up (+) or down (–). For example, the point P corresponds to (4, –3) is 4 right, and 3 down from the origin. Rectangular Coordinate System Example A. Label the points A(-1, 2), B(-3, -2),C(0, -5).
  • 16.
    x = amountto move right (+) or left (–). y = amount to move up (+) or down (–). For example, the point P corresponds to (4, –3) is 4 right, and 3 down from the origin. Rectangular Coordinate System Example A. Label the points A(-1, 2), B(-3, -2),C(0, -5). A
  • 17.
    x = amountto move right (+) or left (–). y = amount to move up (+) or down (–). For example, the point P corresponds to (4, –3) is 4 right, and 3 down from the origin. Rectangular Coordinate System Example A. Label the points A(-1, 2), B(-3, -2),C(0, -5). A B
  • 18.
    x = amountto move right (+) or left (–). y = amount to move up (+) or down (–). For example, the point P corresponds to (4, –3) is 4 right, and 3 down from the origin. Rectangular Coordinate System Example A. Label the points A(-1, 2), B(-3, -2),C(0, -5). A B C
  • 19.
    x = amountto move right (+) or left (–). y = amount to move up (+) or down (–). For example, the point P corresponds to (4, –3) is 4 right, and 3 down from the origin. Rectangular Coordinate System Example A. Label the points A(-1, 2), B(-3, -2),C(0, -5). The ordered pair (x, y) corresponds to a point is called the coordinate of the point, x is the x-coordinate and y is the y-coordinate. A B C
  • 20.
    x = amountto move right (+) or left (–). y = amount to move up (+) or down (–). For example, the point P corresponds to (4, –3) is 4 right, and 3 down from the origin. Rectangular Coordinate System Example A. Label the points A(-1, 2), B(-3, -2),C(0, -5). The ordered pair (x, y) corresponds to a point is called the coordinate of the point, x is the x-coordinate and y is the y-coordinate. A B C Example B: Find the coordinate of P, Q, R as shown. P Q R
  • 21.
    x = amountto move right (+) or left (–). y = amount to move up (+) or down (–). For example, the point P corresponds to (4, –3) is 4 right, and 3 down from the origin. Rectangular Coordinate System Example A. Label the points A(-1, 2), B(-3, -2),C(0, -5). The ordered pair (x, y) corresponds to a point is called the coordinate of the point, x is the x-coordinate and y is the y-coordinate. A B C Example B: Find the coordinate of P, Q, R as shown. P(4, 5), P Q R
  • 22.
    x = amountto move right (+) or left (–). y = amount to move up (+) or down (–). For example, the point P corresponds to (4, –3) is 4 right, and 3 down from the origin. Rectangular Coordinate System Example A. Label the points A(-1, 2), B(-3, -2),C(0, -5). The ordered pair (x, y) corresponds to a point is called the coordinate of the point, x is the x-coordinate and y is the y-coordinate. A B C Example B: Find the coordinate of P, Q, R as shown. P(4, 5), Q(3, -5), P Q R
  • 23.
    x = amountto move right (+) or left (–). y = amount to move up (+) or down (–). For example, the point P corresponds to (4, –3) is 4 right, and 3 down from the origin. Rectangular Coordinate System Example A. Label the points A(-1, 2), B(-3, -2),C(0, -5). The ordered pair (x, y) corresponds to a point is called the coordinate of the point, x is the x-coordinate and y is the y-coordinate. A B C Example B: Find the coordinate of P, Q, R as shown. P(4, 5), Q(3, -5), R(-6, 0) P Q R
  • 24.
    The coordinate ofthe origin is (0, 0). (0,0) Rectangular Coordinate System
  • 25.
    The coordinate ofthe origin is (0, 0). Any point on the x-axis has coordinate of the form (x, 0). (0,0) Rectangular Coordinate System
  • 26.
    The coordinate ofthe origin is (0, 0). Any point on the x-axis has coordinate of the form (x, 0). (5, 0) (0,0) Rectangular Coordinate System
  • 27.
    The coordinate ofthe origin is (0, 0). Any point on the x-axis has coordinate of the form (x, 0). (5, 0)(-6, 0) (0,0) Rectangular Coordinate System
  • 28.
    The coordinate ofthe origin is (0, 0). Any point on the x-axis has coordinate of the form (x, 0). (5, 0)(-6, 0) Any point on the y-axis has coordinate of the form (0, y).(0,0) Rectangular Coordinate System
  • 29.
    The coordinate ofthe origin is (0, 0). Any point on the x-axis has coordinate of the form (x, 0). (5, 0)(-6, 0) Any point on the y-axis has coordinate of the form (0, y). (0, 6) (0,0) Rectangular Coordinate System
  • 30.
    The coordinate ofthe origin is (0, 0). Any point on the x-axis has coordinate of the form (x, 0). (5, 0)(-6, 0) Any point on the y-axis has coordinate of the form (0, y). (0, -4) (0, 6) (0,0) Rectangular Coordinate System
  • 31.
    The coordinate ofthe origin is (0, 0). Any point on the x-axis has coordinate of the form (x, 0). Any point on the y-axis has coordinate of the form (0, y). Rectangular Coordinate System The axes divide the plane into four parts. Counter clockwise, they are denoted as quadrants I, II, III, and IV. QIQII QIII QIV
  • 32.
    The coordinate ofthe origin is (0, 0). Any point on the x-axis has coordinate of the form (x, 0). Any point on the y-axis has coordinate of the form (0, y). Rectangular Coordinate System The axes divide the plane into four parts. Counter clockwise, they are denoted as quadrants I, II, III, and IV. QIQII QIII QIV (+,+)
  • 33.
    The coordinate ofthe origin is (0, 0). Any point on the x-axis has coordinate of the form (x, 0). Any point on the y-axis has coordinate of the form (0, y). Rectangular Coordinate System The axes divide the plane into four parts. Counter clockwise, they are denoted as quadrants I, II, III, and IV. QIQII QIII QIV (+,+)(–,+)
  • 34.
    The coordinate ofthe origin is (0, 0). Any point on the x-axis has coordinate of the form (x, 0). Any point on the y-axis has coordinate of the form (0, y). Rectangular Coordinate System Q1Q2 Q3 Q4 (+,+)(–,+) (–,–) (+,–) The axes divide the plane into four parts. Counter clockwise, they are denoted as quadrants I, II, III, and IV. Respectively, the signs of the coordinates of each quadrant are shown.
  • 35.
    When the x-coordinateof the a point (x, y) is changed to its opposite as (–x , y), the new point is the reflection across the y-axis. (5,4) Rectangular Coordinate System
  • 36.
    When the x-coordinateof the a point (x, y) is changed to its opposite as (–x , y), the new point is the reflection across the y-axis. (5,4)(–5,4) Rectangular Coordinate System
  • 37.
    When the x-coordinateof the a point (x, y) is changed to its opposite as (–x , y), the new point is the reflection across the y-axis. When the y-coordinate of the a point (x, y) is changed to its opposite as (x , –y), the new point is the reflection across the x-axis. (5,4)(–5,4) Rectangular Coordinate System
  • 38.
    When the x-coordinateof the a point (x, y) is changed to its opposite as (–x , y), the new point is the reflection across the y-axis. When the y-coordinate of the a point (x, y) is changed to its opposite as (x , –y), the new point is the reflection across the x-axis. (5,4)(–5,4) (5, –4) Rectangular Coordinate System
  • 39.
    When the x-coordinateof the a point (x, y) is changed to its opposite as (–x , y), the new point is the reflection across the y-axis. When the y-coordinate of the a point (x, y) is changed to its opposite as (x , –y), the new point is the reflection across the x-axis. (5,4)(–5,4) (5, –4) (–x, –y) is the reflection of (x, y) across the origin. Rectangular Coordinate System
  • 40.
    When the x-coordinateof the a point (x, y) is changed to its opposite as (–x , y), the new point is the reflection across the y-axis. When the y-coordinate of the a point (x, y) is changed to its opposite as (x , –y), the new point is the reflection across the x-axis. (5,4)(–5,4) (5, –4) (–x, –y) is the reflection of (x, y) across the origin. (–5, –4) Rectangular Coordinate System
  • 41.
  • 42.
    Movements and Coordinates LetA be the point (2, 3). Rectangular Coordinate System A (2, 3)
  • 43.
    Movements and Coordinates LetA be the point (2, 3). Suppose it’s x–coordinate is increased by 4 to (2 + 4, 3) = (6, 3) Rectangular Coordinate System A (2, 3)
  • 44.
    Movements and Coordinates LetA be the point (2, 3). Suppose it’s x–coordinate is increased by 4 to (2 + 4, 3) = (6, 3) - to the point B, Rectangular Coordinate System A B (2, 3) (6, 3)
  • 45.
    Movements and Coordinates LetA be the point (2, 3). Suppose it’s x–coordinate is increased by 4 to (2 + 4, 3) = (6, 3) - to the point B, this corresponds to moving A to the right by 4. Rectangular Coordinate System A B x–coord. increased by 4 (2, 3) (6, 3)
  • 46.
    Movements and Coordinates LetA be the point (2, 3). Suppose it’s x–coordinate is increased by 4 to (2 + 4, 3) = (6, 3) - to the point B, this corresponds to moving A to the right by 4. Rectangular Coordinate System A B Similarly if the x–coordinate of (2, 3) is decreased by 4 to (2 – 4, 3) = (–2, 3) x–coord. increased by 4 (2, 3) (6, 3)
  • 47.
    Movements and Coordinates LetA be the point (2, 3). Suppose it’s x–coordinate is increased by 4 to (2 + 4, 3) = (6, 3) - to the point B, this corresponds to moving A to the right by 4. Rectangular Coordinate System A B Similarly if the x–coordinate of (2, 3) is decreased by 4 to (2 – 4, 3) = (–2, 3) - to the point C, C x–coord. increased by 4 x–coord. decreased by 4 (2, 3) (6, 3)(–2, 3)
  • 48.
    Movements and Coordinates LetA be the point (2, 3). Suppose it’s x–coordinate is increased by 4 to (2 + 4, 3) = (6, 3) - to the point B, this corresponds to moving A to the right by 4. Rectangular Coordinate System A B Similarly if the x–coordinate of (2, 3) is decreased by 4 to (2 – 4, 3) = (–2, 3) - to the point C, this corresponds to moving A to the left by 4. C x–coord. increased by 4 x–coord. decreased by 4 (2, 3) (6, 3)(–2, 3)
  • 49.
    Movements and Coordinates LetA be the point (2, 3). Suppose it’s x–coordinate is increased by 4 to (2 + 4, 3) = (6, 3) - to the point B, this corresponds to moving A to the right by 4. Rectangular Coordinate System A B Similarly if the x–coordinate of (2, 3) is decreased by 4 to (2 – 4, 3) = (–2, 3) - to the point C, this corresponds to moving A to the left by 4. Hence we conclude that changes in the x–coordinates of a point move the point right and left. C x–coord. increased by 4 x–coord. decreased by 4 (2, 3) (6, 3)(–2, 3)
  • 50.
    Movements and Coordinates LetA be the point (2, 3). Suppose it’s x–coordinate is increased by 4 to (2 + 4, 3) = (6, 3) - to the point B, this corresponds to moving A to the right by 4. Rectangular Coordinate System A B Similarly if the x–coordinate of (2, 3) is decreased by 4 to (2 – 4, 3) = (–2, 3) - to the point C, this corresponds to moving A to the left by 4. Hence we conclude that changes in the x–coordinates of a point move the point right and left. If the x–change is +, the point moves to the right. C x–coord. increased by 4 x–coord. decreased by 4 (2, 3) (6, 3)(–2, 3)
  • 51.
    Movements and Coordinates LetA be the point (2, 3). Suppose it’s x–coordinate is increased by 4 to (2 + 4, 3) = (6, 3) - to the point B, this corresponds to moving A to the right by 4. Rectangular Coordinate System A B Similarly if the x–coordinate of (2, 3) is decreased by 4 to (2 – 4, 3) = (–2, 3) - to the point C, this corresponds to moving A to the left by 4. Hence we conclude that changes in the x–coordinates of a point move the point right and left. If the x–change is +, the point moves to the right. If the x–change is – , the point moves to the left. C x–coord. increased by 4 x–coord. decreased by 4 (2, 3) (6, 3)(–2, 3)
  • 52.
    Again let Abe the point (2, 3). Rectangular Coordinate System A (2, 3)
  • 53.
    Again let Abe the point (2, 3). Suppose its y–coordinate is increased by 4 to (2, 3 + 4) = (2, 7) Rectangular Coordinate System A (2, 3)
  • 54.
    Again let Abe the point (2, 3). Suppose its y–coordinate is increased by 4 to (2, 3 + 4) = (2, 7) - to the point D, Rectangular Coordinate System A D y–coord. increased by 4 (2, 3) (2, 7)
  • 55.
    Again let Abe the point (2, 3). Suppose its y–coordinate is increased by 4 to (2, 3 + 4) = (2, 7) - to the point D, this corresponds to moving A up by 4. Rectangular Coordinate System A D y–coord. increased by 4 (2, 3) (2, 7)
  • 56.
    Again let Abe the point (2, 3). Suppose its y–coordinate is increased by 4 to (2, 3 + 4) = (2, 7) - to the point D, this corresponds to moving A up by 4. Rectangular Coordinate System A D Similarly if the y–coordinate of (2, 3) is decreased by 4 to (2, 3 – 4) = (2, –1) - to the point E, E y–coord. increased by 4 y–coord. decreased by 4 (2, 3) (2, 7) (2, –1)
  • 57.
    Again let Abe the point (2, 3). Suppose its y–coordinate is increased by 4 to (2, 3 + 4) = (2, 7) - to the point D, this corresponds to moving A up by 4. Rectangular Coordinate System A D Similarly if the y–coordinate of (2, 3) is decreased by 4 to (2, 3 – 4) = (2, –1) - to the point E, this corresponds to moving A down by 4. E y–coord. increased by 4 y–coord. decreased by 4 (2, 3) (2, 7) (2, –1)
  • 58.
    Again let Abe the point (2, 3). Suppose its y–coordinate is increased by 4 to (2, 3 + 4) = (2, 7) - to the point D, this corresponds to moving A up by 4. Rectangular Coordinate System A D Similarly if the y–coordinate of (2, 3) is decreased by 4 to (2, 3 – 4) = (2, –1) - to the point E, this corresponds to moving A down by 4. Hence we conclude that changes in the y–coordinates of a point move the point right and left. E y–coord. increased by 4 y–coord. decreased by 4 (2, 3) (2, 7) (2, –1)
  • 59.
    Again let Abe the point (2, 3). Suppose its y–coordinate is increased by 4 to (2, 3 + 4) = (2, 7) - to the point D, this corresponds to moving A up by 4. Rectangular Coordinate System A D Similarly if the y–coordinate of (2, 3) is decreased by 4 to (2, 3 – 4) = (2, –1) - to the point E, this corresponds to moving A down by 4. Hence we conclude that changes in the y–coordinates of a point move the point right and left. If the y–change is +, the point moves up. E y–coord. increased by 4 y–coord. decreased by 4 (2, 3) (2, 7) (2, –1)
  • 60.
    Again let Abe the point (2, 3). Suppose its y–coordinate is increased by 4 to (2, 3 + 4) = (2, 7) - to the point D, this corresponds to moving A up by 4. Rectangular Coordinate System A D Similarly if the y–coordinate of (2, 3) is decreased by 4 to (2, 3 – 4) = (2, –1) - to the point E, this corresponds to moving A down by 4. Hence we conclude that changes in the y–coordinates of a point move the point right and left. If the y–change is +, the point moves up. If the y–change is – , the point moves down. E y–coord. increased by 4 y–coord. decreased by 4 (2, 3) (2, 7) (2, –1)
  • 61.
    Rectangular Coordinate System Example.C. a. Let A be the point (–2, 4). What is the coordinate of the point B that is 100 units directly left of A?
  • 62.
    Rectangular Coordinate System Example.C. a. Let A be the point (–2, 4). What is the coordinate of the point B that is 100 units directly left of A? Moving left corresponds to decreasing the x-coordinate.
  • 63.
    Rectangular Coordinate System Example.C. a. Let A be the point (–2, 4). What is the coordinate of the point B that is 100 units directly left of A? Moving left corresponds to decreasing the x-coordinate. Hence B is (–2 – 100, 4)
  • 64.
    Rectangular Coordinate System Example.C. a. Let A be the point (–2, 4). What is the coordinate of the point B that is 100 units directly left of A? Moving left corresponds to decreasing the x-coordinate. Hence B is (–2 – 100, 4) = (–102, 4).
  • 65.
    Rectangular Coordinate System Example.C. a. Let A be the point (–2, 4). What is the coordinate of the point B that is 100 units directly left of A? Moving left corresponds to decreasing the x-coordinate. Hence B is (–2 – 100, 4) = (–102, 4). b. What is the coordinate of the point C that is 100 units directly above A?
  • 66.
    Rectangular Coordinate System Example.C. a. Let A be the point (–2, 4). What is the coordinate of the point B that is 100 units directly left of A? Moving left corresponds to decreasing the x-coordinate. Hence B is (–2 – 100, 4) = (–102, 4). b. What is the coordinate of the point C that is 100 units directly above A? Moving up corresponds to increasing the y-coordinate.
  • 67.
    Rectangular Coordinate System Example.C. a. Let A be the point (–2, 4). What is the coordinate of the point B that is 100 units directly left of A? Moving left corresponds to decreasing the x-coordinate. Hence B is (–2 – 100, 4) = (–102, 4). b. What is the coordinate of the point C that is 100 units directly above A? Moving up corresponds to increasing the y-coordinate. Hence C is (–2, 4) = (–2, 4 +100)
  • 68.
    Rectangular Coordinate System Example.C. a. Let A be the point (–2, 4). What is the coordinate of the point B that is 100 units directly left of A? Moving left corresponds to decreasing the x-coordinate. Hence B is (–2 – 100, 4) = (–102, 4). b. What is the coordinate of the point C that is 100 units directly above A? Moving up corresponds to increasing the y-coordinate. Hence C is (–2, 4) = (–2, 4 +100) = (–2, 104).
  • 69.
    Rectangular Coordinate System Example.C. a. Let A be the point (–2, 4). What is the coordinate of the point B that is 100 units directly left of A? Moving left corresponds to decreasing the x-coordinate. Hence B is (–2 – 100, 4) = (–102, 4). b. What is the coordinate of the point C that is 100 units directly above A? Moving up corresponds to increasing the y-coordinate. Hence C is (–2, 4) = (–2, 4 +100) = (–2, 104). c. What is the coordinate of the point D that is 50 to the right and 30 below A?
  • 70.
    Rectangular Coordinate System Example.C. a. Let A be the point (–2, 4). What is the coordinate of the point B that is 100 units directly left of A? Moving left corresponds to decreasing the x-coordinate. Hence B is (–2 – 100, 4) = (–102, 4). b. What is the coordinate of the point C that is 100 units directly above A? Moving up corresponds to increasing the y-coordinate. Hence C is (–2, 4) = (–2, 4 +100) = (–2, 104). c. What is the coordinate of the point D that is 50 to the right and 30 below A? We need to add 50 to the x–coordinate (to the right)
  • 71.
    Rectangular Coordinate System Example.C. a. Let A be the point (–2, 4). What is the coordinate of the point B that is 100 units directly left of A? Moving left corresponds to decreasing the x-coordinate. Hence B is (–2 – 100, 4) = (–102, 4). b. What is the coordinate of the point C that is 100 units directly above A? Moving up corresponds to increasing the y-coordinate. Hence C is (–2, 4) = (–2, 4 +100) = (–2, 104). c. What is the coordinate of the point D that is 50 to the right and 30 below A? We need to add 50 to the x–coordinate (to the right) and subtract 30 from the y–coordinate (to go down).
  • 72.
    Rectangular Coordinate System Example.C. a. Let A be the point (–2, 4). What is the coordinate of the point B that is 100 units directly left of A? Moving left corresponds to decreasing the x-coordinate. Hence B is (–2 – 100, 4) = (–102, 4). b. What is the coordinate of the point C that is 100 units directly above A? Moving up corresponds to increasing the y-coordinate. Hence C is (–2, 4) = (–2, 4 +100) = (–2, 104). c. What is the coordinate of the point D that is 50 to the right and 30 below A? We need to add 50 to the x–coordinate (to the right) and subtract 30 from the y–coordinate (to go down). Hence D has coordinate (–2 + 50, 4 – 30)
  • 73.
    Rectangular Coordinate System Example.C. a. Let A be the point (–2, 4). What is the coordinate of the point B that is 100 units directly left of A? Moving left corresponds to decreasing the x-coordinate. Hence B is (–2 – 100, 4) = (–102, 4). b. What is the coordinate of the point C that is 100 units directly above A? Moving up corresponds to increasing the y-coordinate. Hence C is (–2, 4) = (–2, 4 +100) = (–2, 104). c. What is the coordinate of the point D that is 50 to the right and 30 below A? We need to add 50 to the x–coordinate (to the right) and subtract 30 from the y–coordinate (to go down). Hence D has coordinate (–2 + 50, 4 – 30) = (48, –26).
  • 74.
    Exercise. A. a. Writedown the coordinates of the following points. Rectangular Coordinate System AB C D E F G H
  • 75.
    Ex. B. Plotthe following points on the graph paper. Rectangular Coordinate System 2. a. (2, 0) b. (–2, 0) c. (5, 0) d. (–8, 0) e. (–10, 0) All these points are on which axis? 3. a. (0, 2) b. (0, –2) c. (0, 5) d. (0, –6) e. (0, 7) All these points are on which quadrant? 4. a. (5, 2) b. (2, 5) c. (1, 7) d. (7, 1) e. (6, 6) All these points are in which quadrant? 5. a. (–5, –2) b. (–2, –5) c. (–1, –7) d. (–7, –1) e. (–6, –6) All these points are in which quadrant? 6. List three coordinates whose locations are in the 2nd quadrant and plot them. 7. List three coordinates whose locations are in the 4th quadrant and plot them.
  • 76.
    C. Find thecoordinates of the following points. Draw both points for each problem. Rectangular Coordinate System The point that’s 8. 5 units to the right of (3, –2). 10. 4 units to the left of (–1, –5). 9. 6 units to the right of (–4, 2). 11. 6 units to the left of (2, –6). 12. 3 units to the left and 6 units down from (–2, 5). 13. 1 unit to the right and 5 units up from (–3, 1). 14. 3 units to the right and 3 units down from (–3, 4). 15. 2 units to the left and 6 units up from (4, –1).