1 Plotting Points --- In the Cartesian plane This material is the property of the AR Dept. of Education. It may be used and reproduced for non-profit, educational purposes only after contacting the ADE Distance Learning Center. mel

2 First, let’s take a look at….

3 A little history

4 René Descartes ( )

5 A little history René Descartes ( ) philosopher

6 A little history René Descartes ( ) philosopher mathematician

7 A little history René Descartes ( ) philosopher mathematician joined algebra and geometry

8 A little history René Descartes ( ) philosopher mathematician joined algebra and geometry credited with--- Cartesian plane

9 Now, let’s take a look at…

10 Cartesian plane Formed by intersecting two real number lines at right angles

11 Cartesian plane Horizontal axis is usually called the x-axis

12 Cartesian plane Vertical axis is usually called the y-axis

13 Cartesian plane x-y plane Also called:

14 Cartesian plane x-y plane rectangular coordinate system Also called:

15 Now, let’s take a closer look…

16 Cartesian plane Divides into Four Quadrants

17 Cartesian plane Divides into Four Quadrants I

18 Cartesian plane Divides into Four Quadrants I II

19 Cartesian plane Divides into Four Quadrants I II III

20 Cartesian plane Divides into Four Quadrants I II III IV

21 Cartesian plane Divides into Four Quadrants and… I II III IV

22 Cartesian plane The intersection of the two axes is called the origin

23 Cartesian plane Math Alert The quadrants do not include the axes I II III IV

24 Cartesian plane Math Alert A point on the x or y axis is not in a quadrant I II III IV

25 Cartesian plane Each point in the x-y plane is associated with an ordered pair, (x,y) (x,y)

26 The x and y of the ordered pair, (x,y), are called its coordinates Cartesian plane (x,y)

27 Math Alert There is an infinite amount of points in the Cartesian plane Cartesian plane

28 Take note of these graphing basics

29 Always start at (0,0)---every point “originates” at the origin Cartesian plane

30 In plotting (x,y) ---remember the directions of both the x and y axis Cartesian plane y x

31 Cartesian plane (x,---) x-axis goes left and right

32 Cartesian plane (---,y) y-axis goes up and down

33 Now, let’s look at graphing…

34 Now, let’s look at graphing…

35 Cartesian plane Start at (0,0) (, ---) Move right 2 +

36 Cartesian plane (---, ) (---, 1) Move up 1 +

37 Now, let’s look at graphing…

38 Now, let’s look at graphing…

39 Cartesian plane Start at (0,0) (, ---) Move right 4 +

40 Cartesian plane (---, ) (---, -2) Move down 2 -

41 Now, let’s look at graphing…

42 Now, let’s look at graphing…

43 Cartesian plane Start at (0,0) (, ---) Move left 3 -

44 Cartesian plane (---, ) (---, 5) Move up 5 +

45 Now, let’s look at graphing…

46 Now, let’s look at graphing…

47 Cartesian plane Start at (0,0) (none,---) No move right or left

48 Cartesian plane (0, ) (---, 4) Move up 4 +

49 Now, let’s look at graphing…

50 Now, let’s look at graphing…

51 Cartesian plane Start at (0,0) (,---) Move left 5

52 Cartesian plane ( ---, 0) No move up or down

53 Now, let’s look at a little graphing practice…

54 Cartesian plane Approximate the coordinates of the point--- Or what is the ‘(x,y)’of the point? Directions:

55 Cartesian plane Approximate the coordinates of the point Directions:

56 Cartesian plane Approximate the coordinates of the point Directions:

57 Cartesian plane Approximate the coordinates of the point Directions:

58 Cartesian plane Approximate the coordinates of the point Directions:

59 Cartesian plane Approximate the coordinates of the point Directions:

60 Cartesian plane Approximate the coordinates of the point Directions:

61 Cartesian plane Approximate the coordinates of the point Directions:

62 Cartesian plane Approximate the coordinates of the point Directions:

63 Cartesian plane Approximate the coordinates of the point Directions:

64 Cartesian plane Approximate the coordinates of the point Directions:

65 Cartesian plane Approximate the coordinates of the point Directions:

66 Cartesian plane Find the coordinates of the point two units to the left of the y-axis and five units above the x-axis Directions:

67 Cartesian plane Find the coordinates of the point two units to the left of the y-axis and five units above the x-axis Directions:

68 Cartesian plane Find the coordinates of the point on the x-axis and three units to the left of the y-axis Directions:

69 Cartesian plane Find the coordinates of a point on the x- axis and three units to the left of the y-axis Directions:

70 Plotting Points --- In the Cartesian plane This material is the property of the AR Dept. of Education. It may be used and reproduced for non-profit, educational purposes only after contacting the ADE Distance Learning Center. mel

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