5-1: The Coordinate Plane

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5-1 The Coordinate Plane
OBJECTIVES You need to be able to graph ordered
pairs on a coordinate plane.
What is a coordinate plane? Well, it looks like
this
We have the following terms related to the
coordinate plane

• axes - the two perpendicular number lines which
  make up the coordinate plane

one is the x-axis, the other is the y-axis

• origin - the point at the center of the
  coordinate plane (0, 0)
• x-axis - the horizontal number line
• y-axis - the vertical number line
• quadrants - the four regions created by the
  crossing of the two axes

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5-1 The Coordinate Plane
We use coordinates to locate any point in the
coordinate plane.
A coordinate is a point in the plane given by an
ordered pair (x, y) The x tells you how
far right/left the point is from the origin. The
y tells you how far up/down the point is from
the origin. The point (2, 4) would be 2 to the
right and 4 up from the origin. The point (-3, 5)
would be 3 to the left and 5 up from the
origin. The point (4, -2) would be 4 to the right
and 2 down from the origin.
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5-1 The Coordinate Plane
Once you have the basics down, reading and
plotting points on a coordinate plane becomes
easy.
It is critical that you remember x is
horizontal y is vertical x comes first in the
ordered pair y comes second in the ordered
pair (x, y)
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5-1 The Coordinate Plane
EXAMPLE 1 Write ordered pairs for points E, F,
G, and H shown below. Name the quadrant in which
each point is located.
Start with point E. How far right/left do you go
from the origin to get to point E?
right 4
down 2
How far up/down do you go from the origin to get
to point E?
right is positive for x
down is negative for y
so
E (4, -2)
I will use a chart to finish the problem.
To graph an ordered pair means to put a dot at
the coordinate matching the ordered pairs x- and
y-values. The next slide shows how to do this.
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5-1 The Coordinate Plane
EXAMPLE 2 Plot the following points on a
coordinate plane. A. N(-3, -5) B. K(-4.5,
8) C. L(6, 0)
start at the origin
x -3 so move 3 spaces left
B
y -5 so move 5 spaces down
draw a dot at that spot
start at the origin
x -4.5 so move 4.5 spaces left
C
y 8 so move 8 spaces up
draw a dot at that spot
A
start at the origin
x 6 so move 6 spaces right
y 0 so move 0 spaces down/up
draw a dot at that spot
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5-1 The Coordinate Plane
The next example uses graphing, but relates it to
maps and travel.
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5-1 The Coordinate Plane
EXAMPLE 3 Use ordered pairs to name all the
sectors that Interstate Highway 35 passes through
on the map of San Antonio, Texas, shown below.
I-35 begins in the southwest corner and extends
through San Antonio to the northeast corner. Part
of it shares the same path as I-410. I-35 goes
through (1, D), continuing through (2, D), across
the southeast corner of (2, C), turning upward
through (3, C), across the southern portion of
(3, B), sharing the path with I-410 through (4,
B), and exiting the map at the eastern edge of
(4, A).
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5-1 The Coordinate Plane
HOMEWORK
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