end 1 plotting points --- in the cartesian plane this material is the property of the ar dept. of...
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•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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First, let’s take a look at….
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A little history
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A little history
• René Descartes (1596-1650)
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A little history
• René Descartes (1596-1650)
• philosopher
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A little history
• René Descartes (1596-1650)
• philosopher
• mathematician
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A little history
• René Descartes (1596-1650)
• philosopher
• mathematician
• joined algebra and geometry
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A little history
• René Descartes (1596-1650)
• philosopher
• mathematician
• joined algebra and geometry
• credited with---
Cartesian plane
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Now, let’s take a look at…
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Cartesian plane
Formed by
intersecting
two
real number
lines at
right angles
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Cartesian plane
Horizontal axis isusually
called thex-axis
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Cartesian plane
Verticalaxis isusually
called they-axis
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Cartesian plane
• x-y plane
Also called:
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Cartesian plane
• x-y plane
• rectangular
coordinate
system
Also called:
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Now, let’s take a closer look…
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Cartesian plane
Divides into
Four Quadrants
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Cartesian plane
Divides into
Four Quadrants
I
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Cartesian plane
Divides into
Four Quadrants
III
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Cartesian plane
Divides intoFour Quadrants
III
III
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Cartesian plane
Divides intoFour Quadrants
III
III IV
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Cartesian plane
Divides intoFour Quadrants
and…
III
III IV
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Cartesian plane
The intersection
of the two axes is called the
origin
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Cartesian plane
Math AlertThe quadrants do not
include the axes
III
III IV
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Cartesian plane
Math AlertA point on the x or y
axis is not in a quadrant
III
III IV
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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)
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The x and y of the ordered pair,
(x,y), are called its coordinates
Cartesian plane
(x,y)
(x,y)
(x,y)
(x,y)
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Math AlertThere is an infinite
amount of points in the Cartesian
plane
Cartesian plane
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Take note of these graphing basics
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• Always start
at (0,0)---every
point “originates” at the origin
Cartesian plane
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• In plotting (x,y)---remember the
directions of both the x and y
axis
Cartesian planey
x
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Cartesian plane
• (x,---)
x-axis goes
left and right
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Cartesian plane
• (---,y)
y-axis goes
up and down
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Now, let’s look at graphing…
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Now, let’s look at graphing…
(2,1)
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Cartesian plane
• Start at (0,0)
• ( , ---)
• Move right 2
(2,1)+
(2,1)
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Cartesian plane
• (---, )
• (---, 1)
• Move up 1(2,1)
+
(2,1)
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Now, let’s look at graphing…
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Now, let’s look at graphing…
(4, 2)
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Cartesian plane
• Start at (0,0)
• ( , ---)
• Move right 4
+
(4, 2)
(4, 2)
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Cartesian plane
• (---, )
• (---, -2)
• Move down 2
(4, 2)
-
(4, 2)
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Now, let’s look at graphing…
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Now, let’s look at graphing…
( 3,5)
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Cartesian plane
• Start at (0,0)
( , ---)
• Move left 3
( 3,5)-
( 3,5)
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Cartesian plane
• (---, )
• (---, 5)
• Move up 5
+
( 3,5)( 3,5)
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Now, let’s look at graphing…
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Now, let’s look at graphing…
(0,4)
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Cartesian plane
• Start at (0,0)
• (none,---)
• No move right or left
(0,4)
(0,4)
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Cartesian plane
• (0, )
• (---, 4)
• Move up 4
+ (0,4)(0,4)
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Now, let’s look at graphing…
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Now, let’s look at graphing…
( 5,0)
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Cartesian plane
• Start at (0,0)
• ( ,---)
• Move left 5
( 5,0)
( 5,0)
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Cartesian plane
• ( ---, 0)
• No move up
or down
( 5,0)
( 5,0)
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Now, let’s look at a little graphing practice…
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Cartesian plane
Approximate
the coordinates
of the point---
Or what is the
‘(x,y)’of the
point?
Directions:
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Cartesian plane
Approximate
the coordinates
of the point
Directions:
(2,4)
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Cartesian plane
Approximate
the coordinates
of the point
Directions:
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Cartesian plane
Approximate
the coordinates
of the point
Directions:
( 4, 2)
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Cartesian plane
Approximate
the coordinates
of the point
Directions:
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Cartesian plane
Approximate
the coordinates
of the point
Directions:
(0,3)
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Cartesian plane
Approximate
the coordinates
of the point
Directions:
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Cartesian plane
Approximate
the coordinates
of the point
Directions:
(3, 3)
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Cartesian plane
Approximate
the coordinates
of the point
Directions:
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Cartesian plane
Approximate
the coordinates
of the point
Directions:
( 1,6)
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Cartesian plane
Approximate
the coordinates
of the point
Directions:
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Cartesian plane
Approximate
the coordinates
of the point
Directions:
( 5,0)
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Cartesian plane
Find the coordinates of the point two
unitsto the left of they-axis and five units above the
x-axis
Directions:
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Cartesian plane
Find the coordinates of the point two
unitsto the left of they-axis and five units above the
x-axis
Directions:
( 2,5)
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Cartesian plane
Find the
coordinates of
the point on the x-axis and three units to the left
of the
y-axis
Directions:
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Cartesian plane
Find the
coordinates of
a point on the x-axis and three units to the left
of the
y-axis
Directions:
( 3,0)
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•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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