Graphing on the
Cartesian Plane
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The CARTESIAN PLANE
(also called the COORDINATE PLANE)
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The horizontal number line part
of the Cartesian plane is called the X-AXIS.
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The vertical number line part
of the Cartesian plane is called the Y-AXIS.
Origin (0,0)
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The point where the x-axis and y-axis cross is called the ORIGIN
and it has the coordinates (0, 0).
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The four regions (parts) of the Cartesian plane
are called QUADRANTS.
COORDINATES give exact locations for points on the Cartesian plane.�They are always written as ORDERED PAIRS ( X, Y ).
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Coordinates tell us how to get from the ORIGIN (0,0) to a specific location
on the graph. (More on this soon!)
A VERTEX is a point where two sides of a figure (shape) meet.
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Vertex
Did you know?
Some words have plural forms that are
quite different from their singular forms…
SINGULAR PLURAL
One GRAPH Two __________
One AXIS Two __________
One VERTEX Two __________
GRAPHS
VERTICES
AXES
KEY SKILL:
Properly draw a
Cartesian plane.
Label the x-axis, y-axis, origin, and the four quadrants (I, II, III, IV).
EXAMPLE #1
COORDINATES give the exact location for a specific point on the Cartesian plane.
Coordinates are always written as ORDERED PAIRS �in the format (X, Y).
The X-COORDINATE is always given first.
The Y-COORDINATE is always given second.
( x , y )
ORDERED PAIR
(A.K.A. Coordinate Pair or Coordinates)
The x-coordinate tells us the point’s location on the x-axis (horizontal axis).
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y-axis
x-axis
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( x , y )
The y-coordinate tells us the point’s location on the y-axis (vertical axis).
When locating a point on the Cartesian plane, ALWAYS start at the ORIGIN (0,0).
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y-axis
x-axis
If the X-COORDINATE is positive, move to the right.
If the X-COORDINATE is negative, move to the left.
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y-axis
x-axis
If the Y-COORDINATE is positive, move up.
If the Y-COORDINATE is negative, move down.
AFTER you move left or right, it is time to move up or down.
Let’s plot the point ( 3, 2 )
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(3,2)
Always start at the ORIGIN (0,0).
The X-COORDINATE of +3 �tells us to move 3 units in a positive direction (to the right!) along the x-axis.
The Y-COORDINATE of +2 tells us to move 2 units in a positive direction (up!) along the
y-axis.
y-axis
x-axis
Let’s plot the point ( -4, 1 )
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(-4,1)
Always start at the ORIGIN (0,0).
The X-COORDINATE of -4 �tells us to move 4 units in a negative direction (to the left!) along the x-axis.
The Y-COORDINATE of +1 tells us to move 1 unit in a positive direction (up!) along the
y-axis.
y-axis
x-axis
KEY SKILL: Identify the location of a given point using an ordered pair.
EXAMPLE #2: Use ordered pairs to identify the locations of the following points.
( 8, 5 )
( 4, -3 )
( -1, 7 )
( -4, 0 )
KEY SKILL: When given an ordered pair, plot the corresponding point on the Cartesian plane.
A
B
C
D
E
EXAMPLE #3: Plot the following points on the Cartesian plane.
A. ( 4, 2 )
B. ( 0, -2 )
C. ( -5, -3 )
D. ( 6, 0 )
E. ( -7, 1 )
If you look at the possible coordinates (locations) for points
in the four QUADRANTS,�you may notice a pattern!
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y axis
x axis
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(- , -)
(+ , -)
(- , +)
(+ , +)
Graphing on the Cartesian Plane