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. melFirst, let’s take a look at….:
2 First, let’s take a look at….A little history:
3 A little historyA little history:
4 A little history René Descartes (1596-1650)A little history:
5 A little history René Descartes (1596-1650) philosopherA little history:
6 A little history René Descartes (1596-1650) philosopher mathematicianA little history:
7 A little history René Descartes (1596-1650) philosopher mathematician joined algebra and geometryA little history:
8 A little history René Descartes (1596-1650) philosopher mathematician joined algebra and geometry credited with--- Cartesian planeNow, 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 anglesCartesian plane:
11 Cartesian plane Horizontal axis is usually called the x-axisCartesian plane:
12 Cartesian plane Vertical axis is usually called the y-axisCartesian 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 QuadrantsCartesian plane:
17 Cartesian plane Divides into Four Quadrants ICartesian plane:
18 Cartesian plane Divides into Four Quadrants I IICartesian plane:
19 Cartesian plane Divides into Four Quadrants I II IIICartesian plane:
20 Cartesian plane Divides into Four Quadrants I II III IVCartesian plane:
21 Cartesian plane Divides into Four Quadrants and… I II III IVCartesian plane:
22 Cartesian plane The intersection of the two axes is called the originCartesian plane:
23 Cartesian plane Math Alert The quadrants do not include the axes I II III IVCartesian plane:
24 Cartesian plane Math Alert A point on the x or y axis is not in a quadrant I II III IVCartesian 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 planeTake note of these graphing basics :
28 Take note of these graphing basicsCartesian plane:
29 Always start at (0,0) ---every point “originates” at the origin Cartesian planeCartesian plane:
30 In plotting (x,y) ---remember the directions of both the x and y axis Cartesian plane y xCartesian plane:
31 Cartesian plane ( x ,---) x-axis goes left and rightCartesian plane:
32 Cartesian plane ( --- , y ) y-axis goes up and downNow, 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 leftCartesian 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 5Cartesian plane:
52 Cartesian plane ( ---, 0) No move up or downNow, 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. melSlide 71:
71 You can do this!