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!