3 1 rectangular coordinate system

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3 1 rectangular coordinate system

  1. 1. Rectangular Coordinate System Back to 123a-Home
  2. 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. 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. 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. 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. 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. 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. 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. 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. 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. 11. x = amount to move right (+) or left (–). y = amount to move up (+) or down (–). Rectangular Coordinate System
  12. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 24. The coordinate of the origin is (0, 0). (0,0) Rectangular Coordinate System
  25. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 41. Movements and Coordinates Rectangular Coordinate System
  42. 42. Movements and Coordinates Let A be the point (2, 3). Rectangular Coordinate System A (2, 3)
  43. 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. 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. 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. 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. 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. 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. 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. 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. 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. 52. Again let A be the point (2, 3). Rectangular Coordinate System A (2, 3)
  53. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 81. Exercise. A. a. Write down the coordinates of the following points. Rectangular Coordinate System AB C D E F G H
  82. 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. 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).

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