rectangular coordinate system

1. Rectangular Coordinate System
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2. A coordinate system is a system of assigning addresses for
positions in the plane (2 D) or in space (3 D).
Rectangular Coordinate System

3. 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

4. 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

5. 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.

6. 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.

7. 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.

8. 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:

9. 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 (–).

10. 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 (–).

11. x = amount to move
right (+) or left (–).
y = amount to move
up (+) or down (–).
Rectangular Coordinate System

12. 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

13. 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

14. 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

15. 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).

16. 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

17. 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

18. 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

19. 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

20. 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

21. 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

22. 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

23. 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

24. The coordinate of the
origin is (0, 0).
(0,0)
Rectangular Coordinate System

25. 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

26. 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

27. 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

28. 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

29. 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

30. 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

31. 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

32. 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
(+,+)

33. 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
(+,+)(–,+)

34. 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.

35. 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

36. 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

37. 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

38. 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

39. 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

40. 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

41. Movements and Coordinates
Rectangular Coordinate System

42. Movements and Coordinates
Let A be the point (2, 3).
Rectangular Coordinate System
A
(2, 3)

43. 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)

44. 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)

45. 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)

46. 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)

47. 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)

48. 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)

49. 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)

50. 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)

51. 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)

52. Again let A be the point (2, 3).
Rectangular Coordinate System
A
(2, 3)

53. 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)

54. 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)

55. 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)

56. 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)

57. 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)

58. 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)

59. 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)

60. 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)

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?
Here is the vertical format for the calculation:
(–2, 4)
point A

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?
Here is the vertical format for the calculation:
adding 50 to the x–coordinate to move right,
and –30 to the y–coordinate to move down.
(–2, 4)
point A

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?
Here is the vertical format for the calculation:
adding 50 to the x–coordinate to move right,
and –30 to the y–coordinate to move down.
(–2, 4)
+ (50, –30)
+ the “moves”
point A

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?
Here is the vertical format for the calculation:
adding 50 to the x–coordinate to move right,
and –30 to the y–coordinate to move down.
(–2, 4)
+ (50, –30)
(48, –26)
point A
+ the “moves”

74. 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?
Here is the vertical format for the calculation:
adding 50 to the x–coordinate to move right,
and –30 to the y–coordinate to move down.
Hence D has the coordinate (–2 + 50, 4 – 30) = (48, –26).
(–2, 4)
+ (50, –30)
(48, –26)
point A
+ the “moves”

75. Rectangular Coordinate System
d. The point A(–2, 4) is 50 to the right and 30 below the point E
What’s the coordinate of the point E?

76. Rectangular Coordinate System
d. The point A(–2, 4) is 50 to the right and 30 below the point E
What’s the coordinate of the point E?
Let the coordinate of E be (a, b). (a , b) point E

77. Rectangular Coordinate System
d. The point A(–2, 4) is 50 to the right and 30 below the point E
What’s the coordinate of the point E?
Let the coordinate of E be (a, b).
In the vertical format we have:
(a , b)
+ (50, –30)
(–2, 4)
the “moves”
point A
point E

78. Rectangular Coordinate System
d. The point A(–2, 4) is 50 to the right and 30 below the point E
What’s the coordinate of the point E?
Let the coordinate of E be (a, b).
In the vertical format we have
Hence a + 50 = –2 so a = –52
and that b + (–30) = 4 so b = 34.
(a , b)
+ (50, –30)
(–2, 4)
the “moves”
point A
point E

79. Rectangular Coordinate System
d. The point A(–2, 4) is 50 to the right and 30 below the point E
What’s the coordinate of the point E?
Let the coordinate of E be (a, b).
In the vertical format we have
Hence a + 50 = –2 so a = –52
and that b + (–30) = 4 so b = 34.
Hence E is (–52 , 34).
(a , b)
+ (50, –30)
(–2, 4)
the “moves”
point A
point E

80. 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).

81. Exercise. A.
a. Write down the coordinates of the following points.
Rectangular Coordinate System
AB
C
D
E
F
G
H

82. 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.

83. 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).