The Coordinate Plane (Geometry 2_4)

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  1. The Coordinate Plane You will learn to name and graph ordered pairs on a coordinate plane. What You'll Learn In coordinate geometry, grid paper is used to locate points. The plane of the grid is called the coordinate plane .
  2. The Coordinate Plane You will learn to name and graph ordered pairs on a coordinate plane. What You'll Learn In coordinate geometry, grid paper is used to locate points. The plane of the grid is called the coordinate plane . y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3
  3. The Coordinate Plane The horizontal number line is called the ______. y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3 O
  4. The Coordinate Plane The horizontal number line is called the ______. x-axis y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3 O
  5. The Coordinate Plane The horizontal number line is called the ______. x-axis The vertical number line is called the ______. y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3 O
  6. The Coordinate Plane The horizontal number line is called the ______. x-axis The vertical number line is called the ______. y-axis y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3 O
  7. The Coordinate Plane The horizontal number line is called the ______. x-axis The vertical number line is called the ______. y-axis The point of intersection of the two axes is called the _____. y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3 O
  8. The Coordinate Plane The horizontal number line is called the ______. x-axis The vertical number line is called the ______. y-axis The point of intersection of the two axes is called the _____. origin y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3 O
  9. The Coordinate Plane The horizontal number line is called the ______. x-axis The vertical number line is called the ______. y-axis The point of intersection of the two axes is called the _____. origin The two axes separate the plane into four regions called _________. y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3
  10. The Coordinate Plane The horizontal number line is called the ______. x-axis The vertical number line is called the ______. y-axis The point of intersection of the two axes is called the _____. origin The two axes separate the plane into four regions called _________. quadrants y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3 Quadrant I (+, +) Quadrant II ( – , +) Quadrant III ( – , – ) Quadrant IV ( + , – )
  11. The Coordinate Plane An ordered pair of real numbers, called coordinates of a point, locates a point in the coordinate plane.
  12. The Coordinate Plane An ordered pair of real numbers, called coordinates of a point, locates a point in the coordinate plane. Each ordered pair corresponds to EXACTLY ________ in the coordinate plane.
  13. The Coordinate Plane An ordered pair of real numbers, called coordinates of a point, locates a point in the coordinate plane. Each ordered pair corresponds to EXACTLY ________ in the coordinate plane. one point
  14. The Coordinate Plane An ordered pair of real numbers, called coordinates of a point, locates a point in the coordinate plane. Each ordered pair corresponds to EXACTLY ________ in the coordinate plane. one point The point in the coordinate plane is called the graph of the ordered pair.
  15. The Coordinate Plane An ordered pair of real numbers, called coordinates of a point, locates a point in the coordinate plane. Each ordered pair corresponds to EXACTLY ________ in the coordinate plane. one point The point in the coordinate plane is called the graph of the ordered pair. Locating a point on the coordinate plane is called _______ the ordered pair.
  16. The Coordinate Plane An ordered pair of real numbers, called coordinates of a point, locates a point in the coordinate plane. Each ordered pair corresponds to EXACTLY ________ in the coordinate plane. one point The point in the coordinate plane is called the graph of the ordered pair. Locating a point on the coordinate plane is called _______ the ordered pair. graphing
  17. The Coordinate Plane An ordered pair of real numbers, called coordinates of a point, locates a point in the coordinate plane. Each ordered pair corresponds to EXACTLY ________ in the coordinate plane. one point The point in the coordinate plane is called the graph of the ordered pair. Locating a point on the coordinate plane is called _______ the ordered pair. graphing Each point in a coordinate plane corresponds to exactly one __________________________. Each ordered pair of real numbers corresponds to exactly one __________________________. Postulate 2 – 4 Completeness Property for Points in the Plane
  18. The Coordinate Plane An ordered pair of real numbers, called coordinates of a point, locates a point in the coordinate plane. Each ordered pair corresponds to EXACTLY ________ in the coordinate plane. one point The point in the coordinate plane is called the graph of the ordered pair. Locating a point on the coordinate plane is called _______ the ordered pair. graphing ordered pair of real numbers Each point in a coordinate plane corresponds to exactly one __________________________. Each ordered pair of real numbers corresponds to exactly one __________________________. Postulate 2 – 4 Completeness Property for Points in the Plane
  19. The Coordinate Plane An ordered pair of real numbers, called coordinates of a point, locates a point in the coordinate plane. Each ordered pair corresponds to EXACTLY ________ in the coordinate plane. one point The point in the coordinate plane is called the graph of the ordered pair. Locating a point on the coordinate plane is called _______ the ordered pair. graphing ordered pair of real numbers point in the coordinate plane Each point in a coordinate plane corresponds to exactly one __________________________. Each ordered pair of real numbers corresponds to exactly one __________________________. Postulate 2 – 4 Completeness Property for Points in the Plane
  20. The Coordinate Plane Graphing an ordered pair, (point): ( x , y ) Graph point A at (4, 3) The first number, 4, is called the ___________. x-coordinate It tells the number of units the point lies to the __________ of the origin. y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3
  21. The Coordinate Plane Graphing an ordered pair, (point): ( x , y ) Graph point A at (4, 3) The first number, 4, is called the ___________. x-coordinate It tells the number of units the point lies to the __________ of the origin. left or right y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3
  22. The Coordinate Plane Graphing an ordered pair, (point): ( x , y ) Graph point A at (4, 3) The first number, 4, is called the ___________. x-coordinate It tells the number of units the point lies to the __________ of the origin. The second number, 3, is called the ___________. y-coordinate It tells the number of units the point lies _____________ the origin. left or right y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3
  23. The Coordinate Plane Graphing an ordered pair, (point): ( x , y ) Graph point A at (4, 3) The first number, 4, is called the ___________. x-coordinate It tells the number of units the point lies to the __________ of the origin. The second number, 3, is called the ___________. y-coordinate It tells the number of units the point lies _____________ the origin. left or right above or below (4, 3) y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3
  24. The Coordinate Plane Graphing an ordered pair, (point): ( x , y ) Graph point A at (4, 3) The first number, 4, is called the ___________. x-coordinate It tells the number of units the point lies to the __________ of the origin. The second number, 3, is called the ___________. y-coordinate It tells the number of units the point lies _____________ the origin. left or right above or below (4, 3) What is the coordinate of the origin? y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3
  25. The Coordinate Plane Graphing an ordered pair, (point): ( x , y ) Graph point A at (4, 3) The first number, 4, is called the ___________. x-coordinate It tells the number of units the point lies to the __________ of the origin. The second number, 3, is called the ___________. y-coordinate It tells the number of units the point lies _____________ the origin. left or right above or below (4, 3) What is the coordinate of the origin? y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3 (0, 0)
  26. The Coordinate Plane Graphing an ordered pair, (point): ( x , y ) Graph point B at (2, –3) y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3
  27. The Coordinate Plane Graphing an ordered pair, (point): ( x , y ) Graph point B at (2, –3) The first number, 2, is called the ___________. x-coordinate It tells the number of units the point lies to the __________ of the origin. y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3
  28. The Coordinate Plane Graphing an ordered pair, (point): ( x , y ) Graph point B at (2, –3) The first number, 2, is called the ___________. x-coordinate It tells the number of units the point lies to the __________ of the origin. left or right y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3
  29. The Coordinate Plane Graphing an ordered pair, (point): ( x , y ) Graph point B at (2, –3) The first number, 2, is called the ___________. x-coordinate It tells the number of units the point lies to the __________ of the origin. The second number, –3, is called the ___________. y-coordinate It tells the number of units the point lies _____________ the origin. left or right y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3
  30. The Coordinate Plane Graphing an ordered pair, (point): ( x , y ) Graph point B at (2, –3) The first number, 2, is called the ___________. x-coordinate It tells the number of units the point lies to the __________ of the origin. The second number, –3, is called the ___________. y-coordinate It tells the number of units the point lies _____________ the origin. left or right above or below (2, – 3) y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3
  31. The Coordinate Plane Give the coordinates of the points A, B, C, & D Point A(x, y) = Point B(x, y) = Point C(x, y) = Point D(x, y) = A D C B y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3 B C D A
  32. The Coordinate Plane Name the points A, B, C, & D Point A(x, y) = Point B(x, y) = Point C(x, y) = Point D(x, y) = A (3, 2) D C B ( – 3, – 2) ( – 3, 2) (3, – 2) y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3 (–3, 2) B (–3, –2) C (3, –2) D (3, 2) A
  33. The Coordinate Plane Point A(x, y) = A(2, 4) Point B(x, y) = B(2, 0) Point C(x, y) = C(2, – 3) Point D(x, y) = D(2, – 5)
    • On a piece of grid paper draw lines representing the x-axis and the y-axis.
    • Graph :
    y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3
  34. The Coordinate Plane Point A(x, y) = A(2, 4) Point B(x, y) = B(2, 0) Point C(x, y) = C(2, – 3) Point D(x, y) = D(2, – 5)
    • On a piece of grid paper draw lines representing the x-axis and the y-axis.
    • Graph :
    1) What do you notice about the graphs of these points? x = 2 y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3 Consider these questions:
  35. The Coordinate Plane Point A(x, y) = A(2, 4) Point B(x, y) = B(2, 0) Point C(x, y) = C(2, – 3) Point D(x, y) = D(2, – 5)
    • On a piece of grid paper draw lines representing the x-axis and the y-axis.
    • Graph :
    1) What do you notice about the graphs of these points? They lie on a vertical line. x = 2 y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3 Consider these questions:
  36. The Coordinate Plane Point A(x, y) = A(2, 4) Point B(x, y) = B(2, 0) Point C(x, y) = C(2, – 3) Point D(x, y) = D(2, – 5)
    • On a piece of grid paper draw lines representing the x-axis and the y-axis.
    • Graph :
    1) What do you notice about the graphs of these points? They lie on a vertical line. 2) What do you notice about the x-coordinates of these points? x = 2 y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3 Consider these questions:
  37. The Coordinate Plane Point A(x, y) = A(2, 4) Point B(x, y) = B(2, 0) Point C(x, y) = C(2, – 3) Point D(x, y) = D(2, – 5)
    • On a piece of grid paper draw lines representing the x-axis and the y-axis.
    • Graph :
    1) What do you notice about the graphs of these points? They lie on a vertical line. 2) What do you notice about the x-coordinates of these points? They are the same number. x = 2 y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3 Consider these questions:
  38. The Coordinate Plane Point A(x, y) = A(2, 4) Point B(x, y) = B(2, 0) Point C(x, y) = C(2, – 3) Point D(x, y) = D(2, – 5)
    • On a piece of grid paper draw lines representing the x-axis and the y-axis.
    • Graph :
    Write a general statement about ordered pairs that have the same x-coordinate. y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3
  39. The Coordinate Plane Point A(x, y) = A(2, 4) Point B(x, y) = B(2, 0) Point C(x, y) = C(2, – 3) Point D(x, y) = D(2, – 5)
    • On a piece of grid paper draw lines representing the x-axis and the y-axis.
    • Graph :
    Write a general statement about ordered pairs that have the same x-coordinate. x = 2 y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3
  40. The Coordinate Plane Point W(x, y) = W( –4 , – 4) Point X(x, y) = X( –2 , –4 ) Point Y(x, y) = Y(0, –4 ) Point Z(x, y) = Z(3, –4 )
    • Graph :
    On the same coordinate plane y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3
  41. The Coordinate Plane Point W(x, y) = W( –4 , – 4) Point X(x, y) = X( –2 , –4 ) Point Y(x, y) = Y(0, –4 ) Point Z(x, y) = Z(3, –4 )
    • Graph :
    On the same coordinate plane y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3
  42. The Coordinate Plane Point W(x, y) = W( –4 , – 4) Point X(x, y) = X( –2 , –4 ) Point Y(x, y) = Y(0, –4 ) Point Z(x, y) = Z(3, –4 )
    • Graph :
    1) What do you notice about the graphs of these points? On the same coordinate plane y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3 Consider these questions:
  43. The Coordinate Plane Point W(x, y) = W( –4 , – 4) Point X(x, y) = X( –2 , –4 ) Point Y(x, y) = Y(0, –4 ) Point Z(x, y) = Z(3, –4 )
    • Graph :
    1) What do you notice about the graphs of these points? They lie on a horizontal line. On the same coordinate plane y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3 Consider these questions:
  44. The Coordinate Plane Point W(x, y) = W( –4 , – 4) Point X(x, y) = X( –2 , –4 ) Point Y(x, y) = Y(0, –4 ) Point Z(x, y) = Z(3, –4 )
    • Graph :
    1) What do you notice about the graphs of these points? They lie on a horizontal line. 2) What do you notice about the y-coordinates of these points? On the same coordinate plane y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3 Consider these questions:
  45. The Coordinate Plane Point W(x, y) = W( –4 , – 4) Point X(x, y) = X( –2 , –4 ) Point Y(x, y) = Y(0, –4 ) Point Z(x, y) = Z(3, –4 )
    • Graph :
    1) What do you notice about the graphs of these points? They lie on a horizontal line. 2) What do you notice about the y-coordinates of these points? They are the same number. On the same coordinate plane y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3 Consider these questions:
  46. The Coordinate Plane Point W(x, y) = W( –4 , – 4) Point X(x, y) = X( –2 , –4 ) Point Y(x, y) = Y(0, –4 ) Point Z(x, y) = Z(3, –4 )
    • Graph :
    Write a general statement about ordered pairs that have the same y-coordinate. On the same coordinate plane y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3
  47. The Coordinate Plane Point W(x, y) = W( –4 , – 4) Point X(x, y) = X( –2 , –4 ) Point Y(x, y) = Y(0, –4 ) Point Z(x, y) = Z(3, –4 )
    • Graph :
    Write a general statement about ordered pairs that have the same y-coordinate. y = – 4 On the same coordinate plane y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3
  48. The Coordinate Plane If a and b are real numbers, a vertical line contains all points (x, y) such that _____ and a horizontal line contains all points (x, y) such that _____ Theorem 2 – 4
  49. The Coordinate Plane x = a y = b If a and b are real numbers, a vertical line contains all points (x, y) such that _____ and a horizontal line contains all points (x, y) such that _____ Theorem 2 – 4
  50. The Coordinate Plane x = a y = b Graph the lines: x = –3 If a and b are real numbers, a vertical line contains all points (x, y) such that _____ and a horizontal line contains all points (x, y) such that _____ Theorem 2 – 4 y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3
  51. The Coordinate Plane x = a y = b Graph the lines: x = –3 If a and b are real numbers, a vertical line contains all points (x, y) such that _____ and a horizontal line contains all points (x, y) such that _____ Theorem 2 – 4 y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3
  52. The Coordinate Plane x = a y = b Graph the lines: x = –3 y = 2 If a and b are real numbers, a vertical line contains all points (x, y) such that _____ and a horizontal line contains all points (x, y) such that _____ Theorem 2 – 4 y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3
  53. The Coordinate Plane x = a y = b Graph the lines: x = –3 y = 2 If a and b are real numbers, a vertical line contains all points (x, y) such that _____ and a horizontal line contains all points (x, y) such that _____ Theorem 2 – 4 y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3
  54. The Coordinate Plane x = a y = b Graph the lines: x = –3 y = 2 Graph the point of intersection of these lines. If a and b are real numbers, a vertical line contains all points (x, y) such that _____ and a horizontal line contains all points (x, y) such that _____ Theorem 2 – 4 y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3
  55. The Coordinate Plane x = a y = b Graph the lines: x = –3 y = 2 Graph the point of intersection of these lines. If a and b are real numbers, a vertical line contains all points (x, y) such that _____ and a horizontal line contains all points (x, y) such that _____ Theorem 2 – 4 y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3 (–3, 2)
  56. The Coordinate Plane End of Lesson