Cartesian Plane 1

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Slide 1:

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

First, let’s take a look at….:

2 First, let’s take a look at….

A little history:

3 A little history

A little history:

4 A little history René Descartes (1596-1650)

A little history:

5 A little history René Descartes (1596-1650) philosopher

A little history:

6 A little history René Descartes (1596-1650) philosopher mathematician

A little history:

7 A little history René Descartes (1596-1650) philosopher mathematician joined algebra and geometry

A little history:

8 A little history René Descartes (1596-1650) philosopher mathematician joined algebra and geometry credited with--- Cartesian plane

Now, let’s take a look at… :

9 Now, let’s take a look at…

Cartesian plane:

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

Cartesian plane:

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

Cartesian plane:

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

Cartesian plane:

13 Cartesian plane x-y plane Also called :

Cartesian plane:

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

Now, let’s take a closer look… :

15 Now, let’s take a closer look…

Cartesian plane:

16 Cartesian plane Divides into Four Quadrants

Cartesian plane:

17 Cartesian plane Divides into Four Quadrants I

Cartesian plane:

18 Cartesian plane Divides into Four Quadrants I II

Cartesian plane:

19 Cartesian plane Divides into Four Quadrants I II III

Cartesian plane:

20 Cartesian plane Divides into Four Quadrants I II III IV

Cartesian plane:

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

Cartesian plane:

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

Cartesian plane:

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

Cartesian plane:

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

Cartesian plane:

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

Cartesian plane:

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

Cartesian plane:

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

Take note of these graphing basics :

28 Take note of these graphing basics

Cartesian plane:

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

Cartesian plane:

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

Cartesian plane:

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

Cartesian plane:

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

Now, let’s look at graphing… :

33 Now, let’s look at graphing…

Now, let’s look at graphing… :

34 Now, let’s look at graphing…

Cartesian plane:

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

Cartesian plane:

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

Now, let’s look at graphing… :

37 Now, let’s look at graphing…

Now, let’s look at graphing… :

38 Now, let’s look at graphing…

Cartesian plane:

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

Cartesian plane:

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

Now, let’s look at graphing… :

41 Now, let’s look at graphing…

Now, let’s look at graphing… :

42 Now, let’s look at graphing…

Cartesian plane:

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

Cartesian plane:

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

Now, let’s look at graphing… :

45 Now, let’s look at graphing…

Now, let’s look at graphing… :

46 Now, let’s look at graphing…

Cartesian plane:

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

Cartesian plane:

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

Now, let’s look at graphing… :

49 Now, let’s look at graphing…

Now, let’s look at graphing… :

50 Now, let’s look at graphing…

Cartesian plane:

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

Cartesian plane:

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

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

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

Cartesian plane:

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

Cartesian plane:

55 Cartesian plane Approximate the coordinates of the point Directions:

Cartesian plane:

56 Cartesian plane Approximate the coordinates of the point Directions:

Cartesian plane:

57 Cartesian plane Approximate the coordinates of the point Directions:

Cartesian plane:

58 Cartesian plane Approximate the coordinates of the point Directions:

Cartesian plane:

59 Cartesian plane Approximate the coordinates of the point Directions:

Cartesian plane:

60 Cartesian plane Approximate the coordinates of the point Directions:

Cartesian plane:

61 Cartesian plane Approximate the coordinates of the point Directions:

Cartesian plane:

62 Cartesian plane Approximate the coordinates of the point Directions:

Cartesian plane:

63 Cartesian plane Approximate the coordinates of the point Directions:

Cartesian plane:

64 Cartesian plane Approximate the coordinates of the point Directions:

Cartesian plane:

65 Cartesian plane Approximate the coordinates of the point Directions:

Cartesian plane:

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:

Cartesian plane:

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:

Cartesian plane:

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

Cartesian plane:

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

Slide 70:

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

Slide 71:

71 You can do this!

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