Upload
mohde4
View
224
Download
0
Embed Size (px)
Citation preview
8/10/2019 Cartesian Plane 1
1/71
End1
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
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
2/71
End2
First, lets take a look at.
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
3/71
End3
A little history
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
4/71
End4
A little history
Ren Descartes
(1596-1650)
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
5/71
End5
A little history
Ren Descartes
(1596-1650)
philosopher
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
6/71
End6
A little history
Ren Descartes
(1596-1650)
philosopher
mathematician
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
7/71End 7
A little history
Ren Descartes
(1596-1650)
philosopher
mathematician
joined algebra
and geometry
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
8/71End
8
A little history
Ren Descartes
(1596-1650)
philosopher
mathematician
joined algebra
and geometry credited with---
Cartesian plane
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
9/71End
9
Now, lets take a look at
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
10/71End
10
Cartesian plane
Formed by
intersecting
tworeal number
lines at
right angles
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
11/71End
11
Cartesian plane
Horizontal
axis is
usually
called thex-axis
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
12/71End
12
Cartesian plane
Verticalaxis is
usually
called the
y-axis
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
13/71
End13
Cartesian plane
x-y plane
Also called:
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
14/71
End14
Cartesian plane
x-y plane
rectangular
coordinate
system
Also called:
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
15/71
End15
Now, lets take a closer look
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
16/71
End16
Cartesian plane
Divides intoFour Quadrants
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
17/71
End17
Cartesian plane
Divides intoFour Quadrants
I
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
18/71
End18
Cartesian plane
Divides intoFour Quadrants
III
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
19/71
End19
Cartesian plane
Divides into
Four Quadrants
III
III
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
20/71
End20
Cartesian plane
Divides into
Four Quadrants
III
III IV
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
21/71
End21
Cartesian plane
Divides intoFour Quadrants
and
III
III IV
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
22/71
End22
Cartesian plane
The intersection
of the two axesis called the
origin
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
23/71
End23
Cartesian plane
Math Alert
The quadrantsdonotinclude the
axes
III
III IV
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
24/71
End24
Cartesian plane
Math Alert
A pointon the xoryaxis is notin a
quadrant
III
III IV
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
25/71
End25
Cartesian plane
Eachpointin the
x-y planeis
associated withan orderedpair,
(x,y)
(x,y)
(x,y)
(x,y)
(x,y)
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
26/71
End26
The xand yof theorderedpair,
(x,y),are called itscoordinates
Cartesian plane
(x,y)
(x,y)
(x,y)
(x,y)
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
27/71
End27
Math Alert
There is an infiniteamount of pointsin the Cartesian
plane
Cartesian plane
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
28/71
End28
Take note of these graphing basics
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
29/71
End29
Always start
at (0,0)---everypoint originates
at the origin
Cartesian plane
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
30/71
End30
In plotting (x,y)
---remember thedirectionsofboth the xand y
axis
Cartesian plane
y
x
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
31/71
End31
Cartesian plane
(x,---)
x-axisgoes
leftand right
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
32/71
End32
Cartesian plane
(---,y)
y-axisgoes
upand down
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
33/71
End33
Now, lets look at graphing
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
34/71
End34
Now, lets look at graphing
(2,1)
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
35/71
End35
Cartesian plane
Start at (0,0)
( , ---)
Move right
2
(2,1)+
(2,1)
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
36/71
End36
Cartesian plane
(---, )
(---, 1)
Move up1(2,1)
+
(2,1)
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
37/71
End37
Now, lets look at graphing
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
38/71
End38
Now, lets look at graphing
(4, 2)
i l
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
39/71
End39
Cartesian plane
Start at (0,0)
( , ---)
Move right4
+
(4, 2)
(4, 2)
C i l
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
40/71
End40
Cartesian plane
(---, )
(---, -2) Move down 2
(4, 2)
-
(4, 2)
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
41/71
End41
Now, lets look at graphing
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
42/71
End42
Now, lets look at graphing
( 3,5)
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
43/71
C i l
8/10/2019 Cartesian Plane 1
44/71
End44
Cartesian plane
(---, )
(---, 5)
Move up5
+
( 3,5)( 3,5)
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
45/71
End45
Now, lets look at graphing
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
46/71
End46
Now, lets look at graphing
(0,4)
C t i l
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
47/71
End47
Cartesian plane
Start at (0,0)
(none,---)
Nomove
right or left
(0,4)
(0,4)
C t i l
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
48/71
End48
Cartesian plane
(0, )
(---, 4)
Move up4
+ (0,4)(0,4)
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
49/71
End49
Now, lets look at graphing
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
50/71
End50
Now, lets look at graphing
( 5,0)
C t i l
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
51/71
End51
Cartesian plane
Start at (0,0)
( ,---)
Move left5
( 5,0)
( 5,0)
C t i l
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
52/71
End52
Cartesian plane
( ---, 0)
Nomove up
or down
( 5,0)
( 5,0)
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
53/71
End53
Now, lets look at a little
graphing practice
Cartesian plane
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
54/71
End54
Cartesian plane
Approximate
the coordinates
of thepoint---
Or what is the
(x,y)of the
point?
Directions:
Cartesian plane
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
55/71
End55
Cartesian plane
Approximate
the coordinates
of thepoint
Directions:
(2,4)
Cartesian plane
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
56/71
End56
Cartesian plane
Approximate
the coordinates
of thepoint
Directions:
Cartesian plane
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
57/71
End57
Cartesian plane
Approximate
the coordinates
of thepoint
Directions:
( 4, 2)
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
58/71
Cartesian plane
8/10/2019 Cartesian Plane 1
59/71
End59
Cartesian plane
Approximate
the coordinates
of thepoint
Directions:
(0,3)
Cartesian plane
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
60/71
End60
Cartesian plane
Approximate
the coordinates
of thepoint
Directions:
Cartesian plane
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
61/71
End61
Cartesian plane
Approximate
the coordinates
of thepoint
Directions:
(3, 3)
Cartesian plane
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
62/71
End62
Cartesian plane
Approximate
the coordinates
of thepoint
Directions:
Cartesian plane
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
63/71
End63
Cartesian plane
Approximate
the coordinates
of thepoint
Directions:
( 1, 6)
Cartesian plane
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
64/71
End64
Cartesian plane
Approximate
the coordinates
of thepoint
Directions:
Cartesian plane
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
65/71
End65
Cartesian plane
Approximate
the coordinates
of thepoint
Directions:
( 5, 0)
Cartesian plane
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
66/71
End66
Cartesian plane
Find thecoordinates of
thepointtwo
unitsto the left of the
y-axis and five
units above thex-axis
Directions:
Cartesian plane
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
67/71
End67
Cartesian plane
Find thecoordinates of
thepointtwo
unitsto the left of the
y-axis and five
units above thex-axis
Directions:
( 2,5)
Cartesian plane
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
68/71
End68
Cartesian plane
Find the
coordinates of
thepointon the
x-axis and three
units to the left
of the
y-axis
Directions:
Cartesian plane
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
69/71
End69
Cartesian plane
Find the
coordinates of
apointon the x-
axis and three
units to the left
of the
y-axis
Directions:
( 3, 0)
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
70/71
End70
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
http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm8/10/2019 Cartesian Plane 1
71/71