Download Ch 7-1 The Coordinate Plane

7-1 The Coordinate Plane
California
Standards
Preparation for
AF3.3 Graph linear
functions, noting that the vertical change (change
in y-value) per unit of horizontal change (change in
x-value) is always the same and know that the ratio
(“rise over run”) is called the slope of a graph.
Holt CA Course 1
7-1 The Coordinate Plane
A coordinate plane is a
4
plane containing a
Quadrant II 3
horizontal number line,
2
1
the x-axis, and a vertical
0
number line, the y-axis.
–5 –4 –3 –2 –1
–1
The intersection of these
–2
axes is called the origin. Quadrant III–3
5
y
y-axis
Quadrant I
x-axis
x
1 2 3
Origin
Quadrant IV
–4
–5
The axes divide the coordinate plane into four
regions called quadrants.
Holt CA Course 1
4 5
7-1 The Coordinate Plane
Additional Example 1: Identifying Quadrants on a
Coordinate Plane
Identify the quadrant that contains each point.
5
A. S
S lies in quadrant IV.
B. T
T lies in quadrant I.
4
3
2
W
T
1
0
–5 –4 –3 –2 –1
–1
–2
C. W
W lies on the y-axis
between Quadrants I and II
Holt CA Course 1
y
–3
–4
–5
x
1 2 3
4 5
S
7-1 The Coordinate Plane
Check It Out! Example 1
Identify the quadrant that contains each point.
5
A. N
N
N lies in quadrant II.
B. X
X lies in quadrant III.
C. Y
Y lies on the origin.
4
3
2
1
0
–5 –4 –3 –2 –1
–1
–2
X
–3
–4
–5
Holt CA Course 1
y
Y
x
1 2 3
4 5
7-1 The Coordinate Plane
An ordered pair is a pair of
numbers (x, y) that can be
used to locate a point on a
coordinate plane. The two
numbers that form the ordered
–5
pair are called coordinates.
The origin is identified by the
ordered pair (0,0).
5
4
3
2
2 units
up
x
1
0
–4 –3 –2 –1
–1
–2
Ordered pair
(3, 2)
x-coordinate
y-coordinate
Units up
Units right
or left from 0 or down from 0
Holt CA Course 1
y
–3
–4
–5
1 2 3
3 units
right
4 5
7-1 The Coordinate Plane
Additional Example 2: Plotting Points on a
Coordinate Plane
Plot each point on a
y
coordinate plane.
5
A. D (3, 3)
Start at the origin. Move
3 units right and 3 units up.
B. E (–2, –3)
4
3
2
1
0
–5 –4 –3 –2 –1
–1
–2
Start at the origin. Move
2 units left and 3 units down.
C. F (3, –5)
Start at the origin. Move
3 units right and 5 units down.
Holt CA Course 1
D
x
1 2 3
4 5
E–3
–4
–5
F
7-1 The Coordinate Plane
Check It Out! Example 2
Plot each point on a
coordinate plane.
A. D (4, 4)
Start at the origin. Move
4 units right and 4 units up.
B. E (–2, 3)
Start at the origin. Move
2 units left and 3 units up.
C. F (–1, –2)
Start at the origin. Move
1 unit left and 2 units down.
Holt CA Course 1
5
E
y
4
3
D
2
1
0
–5 –4 –3 –2 –1
–1
–2
F
–3
–4
–5
x
1 2 3
4 5
7-1 The Coordinate Plane
Additional Example 3: Identifying Points on a
Coordinate Plane
Give the coordinates
of each point.
y
5
X 4
A. X
(–2, 5)
3
Start at the origin. Point X
is 2 units left and 5 units up.
B. Y
(–1, 0)
2
Y
0
–5 –4 –3 –2 –1
–1
–2
Start at the origin. Point Y is
one unit left on the x-axis.
C. Z
(3, –3)
Start at the origin. Point Z is 3 units
right and 3 units down.
Holt CA Course 1
1
–3
–4
–5
x
1 2 3
4 5
Z
7-1 The Coordinate Plane
Check It Out! Example 3
Give the coordinates
of each point.
A. L
(–4, 3)
Start at the origin. Point L
is 4 units left and 3 units up.
B. M
(–2, –2)
5
4
3
L
y
N
2
1
0
–5 –4 –3 –2 –1
–1
–2
M
x
1 2 3
–3
Start at the origin. Point M is
–4
2 units left and 2 units down.
–5
C. N
(3, 4)
Start at the origin. Point N is 3 units right and 4
units up.
Holt CA Course 1
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