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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) <ul><li>On a piece of grid paper draw lines representing the x-axis and the y-axis. </li></ul><ul><li>Graph : </li></ul>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) <ul><li>On a piece of grid paper draw lines representing the x-axis and the y-axis. </li></ul><ul><li>Graph : </li></ul>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) <ul><li>On a piece of grid paper draw lines representing the x-axis and the y-axis. </li></ul><ul><li>Graph : </li></ul>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) <ul><li>On a piece of grid paper draw lines representing the x-axis and the y-axis. </li></ul><ul><li>Graph : </li></ul>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) <ul><li>On a piece of grid paper draw lines representing the x-axis and the y-axis. </li></ul><ul><li>Graph : </li></ul>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) <ul><li>On a piece of grid paper draw lines representing the x-axis and the y-axis. </li></ul><ul><li>Graph : </li></ul>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) <ul><li>On a piece of grid paper draw lines representing the x-axis and the y-axis. </li></ul><ul><li>Graph : </li></ul>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 ) <ul><li>Graph : </li></ul>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 ) <ul><li>Graph : </li></ul>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 ) <ul><li>Graph : </li></ul>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 ) <ul><li>Graph : </li></ul>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 ) <ul><li>Graph : </li></ul>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 ) <ul><li>Graph : </li></ul>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 ) <ul><li>Graph : </li></ul>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 ) <ul><li>Graph : </li></ul>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

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I am also planning in the next few weeks to do lessons on Linear Graphs for my students, which you may also find useful. Thanks again for such a fabulous resource. - Passy.

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