The Coordinate Plane
1.8
The Coordinate Plane Goal: Identify and plot points in a coordinate plane.
Vocabulary Coordinate plane:
x-axis:
y-axis:
Origin:
Quadrant:
Ordered pair:
x-coordinate:
y-coordinate:
Scatter plot:
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Chapter 1 • Pre-Algebra Notetaking Guide
17
1.8
The Coordinate Plane Goal: Identify and plot points in a coordinate plane.
Vocabulary Coordinate plane:
A coordinate plane is formed by the intersection of a horizontal number line and a vertical number line.
x-axis: The horizontal axis in a coordinate plane
y-axis: The vertical axis in a coordinate plane
Origin:
The point (0, 0) in a coordinate plane at which the horizontal axis intersects the vertical axis
Quadrant:
One of four parts into which the axes divide the coordinate plane
Ordered pair:
Each point in the coordinate plane corresponds to a pair of real numbers that gives the location of the point on the plane.
x-coordinate:
The first number in an ordered pair is the x-coordinate.
y-coordinate:
The second number in an ordered pair is the y-coordinate.
Scatter plot:
A scatter plot uses a coordinate plane to display paired data.
Copyright © Holt McDougal. All rights reserved.
Chapter 1 • Pre-Algebra Notetaking Guide
17
Naming Points in a Coordinate Plane
Example 1
Give the coordinates of the point. a. A b. B y 4
A
3 2 1
4 3 2
O
1
2
x
3
B
2 3 4
Solution a. Point A is
units to the
The x-coordinate is coordinates are b. Point B is
of the origin and
and the y-coordinate is
(
. The
of the origin and
. The x-coordinate is
(
.
).
,
units to the
The coordinates are
units
,
unit
and the y-coordinate is
.
).
Checkpoint Give the coordinates of the point.
1. C
y 4 3 2
2. D
1
C 4 3 2
D
3. E
18
Chapter 1 • Notetaking Guide
O
1
2
3
4 x
2 3 4
E
Copyright © Holt McDougal. All rights reserved.
Naming Points in a Coordinate Plane
Example 1
Give the coordinates of the point. a. A b. B y 4
A
3 2 1
4 3 2
O
1
2
x
3
2
B
3 4
Solution a. Point A is 2 units to the left of the origin and 3 units up . The x-coordinate is 2 and the y-coordinate is 3 . The coordinates are
( 2 ,
)
3 .
b. Point B is 4 units to the right of the origin and 1 unit down . The x-coordinate is 4 and the y-coordinate is 1 .
The coordinates are
(4
)
, 1 .
Checkpoint Give the coordinates of the point.
1. C
y 4 3
(2, 0)
2
2. D
1
C 4 3 2
(4, 3)
3. E
D
O
1
2
3
4 x
2 3 4
E
(2, 4)
18
Chapter 1 • Notetaking Guide
Copyright © Holt McDougal. All rights reserved.
Plotting Points in a Coordinate Plane
Example 2
Plot the point in the coordinate plane. Describe the location of the point. a. A(2, 3) b. B(4, 0) c. C(1, 3) y 4 3 2 1 4 3 2
O
1
2
3
4 x
2 3 4
Solution a. Begin at the origin and move units
units to the
. Point A is located
b. Begin at the origin and move located
.
units to the
. Point B is
.
c. Begin at the origin and move units
, then move
unit to the
, then move
. Point C is located
.
Checkpoint Plot the point in the coordinate plane. Describe the
location of the point. 4. D(0, 3)
y 4 3 2
5. E(2, 4)
1 4 3 2
O
1
2
3
4 x
2
6. F(1, 2)
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3 4
Chapter 1 • Pre-Algebra Notetaking Guide
19
Plotting Points in a Coordinate Plane
Example 2
Plot the point in the coordinate plane. Describe the location of the point. a. A(2, 3) b. B(4, 0) c. C(1, 3) y 4
A (2, 3)
3 2 1
B (4, 0) 4 3 2
O 2 3
1
2
3
4 x
C (1, 3)
4
Solution a. Begin at the origin and move 2 units to the right , then move 3 units up . Point A is located in Quadrant I .
b. Begin at the origin and move 4 units to the left . Point B is located on the x-axis . c. Begin at the origin and move 1 unit to the right , then move 3 units down . Point C is located in Quadrant IV .
Checkpoint Plot the point in the coordinate plane. Describe the
location of the point. 4. D(0, 3) Point D is located on the y-axis.
y 4
F (1, 2)
5. E(2, 4)
3
D (0, 3)
2 1
4 3 2
Point E is located in Quadrant III.
O
1
2
3
4 x
2 3
6. F(1, 2) E (2, 4)
4
Point F is located in Quadrant II.
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Chapter 1 • Pre-Algebra Notetaking Guide
19
Example 3
Making a Scatter Plot
The number of hours you spent studying for 5 different math tests and the score you got on each test is given in the table. Make a scatter plot of the data and describe any relationship you see. Hours studying
1
3
4
4
5
Test score
55
78
86
89
98
Solution 1. Write the data as ordered pairs. Let the x-coordinate represent the hours spent studying, and let the y-coordinate represent the test score: . 2. Plot the ordered pairs in a coordinate plane. You need only the first quadrant. 100 90 80 Test score
70 60 50 40 30 20 10 0
0 1 2 3 4 5 6 Hours studying
Notice that the points the hours spent studying
20
Chapter 1 • Notetaking Guide
from left to right. You can conclude as , your test scores
.
Copyright © Holt McDougal. All rights reserved.
Example 3
Making a Scatter Plot
The number of hours you spent studying for 5 different math tests and the score you got on each test is given in the table. Make a scatter plot of the data and describe any relationship you see. Hours studying
1
3
4
4
5
Test score
55
78
86
89
98
Solution 1. Write the data as ordered pairs. Let the x-coordinate represent the hours spent studying, and let the y-coordinate represent the test score: (1, 55), (3, 78), (4, 86), (4, 89), (5, 98) . 2. Plot the ordered pairs in a coordinate plane. You need only the first quadrant. 100 90 80 Test score
70 60 50 40 30 20 10 0
0 1 2 3 4 5 6 Hours studying
Notice that the points rise from left to right. You can conclude as the hours spent studying increases , your test scores increase .
20
Chapter 1 • Notetaking Guide
Copyright © Holt McDougal. All rights reserved.
The Coordinate Plane Goal: Identify and plot points in a coordinate plane.
Vocabulary Coordinate plane:
x-axis:
y-axis:
Origin:
Quadrant:
Ordered pair:
x-coordinate:
y-coordinate:
Scatter plot:
Copyright © Holt McDougal. All rights reserved.
Chapter 1 • Pre-Algebra Notetaking Guide
17
1.8
The Coordinate Plane Goal: Identify and plot points in a coordinate plane.
Vocabulary Coordinate plane:
A coordinate plane is formed by the intersection of a horizontal number line and a vertical number line.
x-axis: The horizontal axis in a coordinate plane
y-axis: The vertical axis in a coordinate plane
Origin:
The point (0, 0) in a coordinate plane at which the horizontal axis intersects the vertical axis
Quadrant:
One of four parts into which the axes divide the coordinate plane
Ordered pair:
Each point in the coordinate plane corresponds to a pair of real numbers that gives the location of the point on the plane.
x-coordinate:
The first number in an ordered pair is the x-coordinate.
y-coordinate:
The second number in an ordered pair is the y-coordinate.
Scatter plot:
A scatter plot uses a coordinate plane to display paired data.
Copyright © Holt McDougal. All rights reserved.
Chapter 1 • Pre-Algebra Notetaking Guide
17
Naming Points in a Coordinate Plane
Example 1
Give the coordinates of the point. a. A b. B y 4
A
3 2 1
4 3 2
O
1
2
x
3
B
2 3 4
Solution a. Point A is
units to the
The x-coordinate is coordinates are b. Point B is
of the origin and
and the y-coordinate is
(
. The
of the origin and
. The x-coordinate is
(
.
).
,
units to the
The coordinates are
units
,
unit
and the y-coordinate is
.
).
Checkpoint Give the coordinates of the point.
1. C
y 4 3 2
2. D
1
C 4 3 2
D
3. E
18
Chapter 1 • Notetaking Guide
O
1
2
3
4 x
2 3 4
E
Copyright © Holt McDougal. All rights reserved.
Naming Points in a Coordinate Plane
Example 1
Give the coordinates of the point. a. A b. B y 4
A
3 2 1
4 3 2
O
1
2
x
3
2
B
3 4
Solution a. Point A is 2 units to the left of the origin and 3 units up . The x-coordinate is 2 and the y-coordinate is 3 . The coordinates are
( 2 ,
)
3 .
b. Point B is 4 units to the right of the origin and 1 unit down . The x-coordinate is 4 and the y-coordinate is 1 .
The coordinates are
(4
)
, 1 .
Checkpoint Give the coordinates of the point.
1. C
y 4 3
(2, 0)
2
2. D
1
C 4 3 2
(4, 3)
3. E
D
O
1
2
3
4 x
2 3 4
E
(2, 4)
18
Chapter 1 • Notetaking Guide
Copyright © Holt McDougal. All rights reserved.
Plotting Points in a Coordinate Plane
Example 2
Plot the point in the coordinate plane. Describe the location of the point. a. A(2, 3) b. B(4, 0) c. C(1, 3) y 4 3 2 1 4 3 2
O
1
2
3
4 x
2 3 4
Solution a. Begin at the origin and move units
units to the
. Point A is located
b. Begin at the origin and move located
.
units to the
. Point B is
.
c. Begin at the origin and move units
, then move
unit to the
, then move
. Point C is located
.
Checkpoint Plot the point in the coordinate plane. Describe the
location of the point. 4. D(0, 3)
y 4 3 2
5. E(2, 4)
1 4 3 2
O
1
2
3
4 x
2
6. F(1, 2)
Copyright © Holt McDougal. All rights reserved.
3 4
Chapter 1 • Pre-Algebra Notetaking Guide
19
Plotting Points in a Coordinate Plane
Example 2
Plot the point in the coordinate plane. Describe the location of the point. a. A(2, 3) b. B(4, 0) c. C(1, 3) y 4
A (2, 3)
3 2 1
B (4, 0) 4 3 2
O 2 3
1
2
3
4 x
C (1, 3)
4
Solution a. Begin at the origin and move 2 units to the right , then move 3 units up . Point A is located in Quadrant I .
b. Begin at the origin and move 4 units to the left . Point B is located on the x-axis . c. Begin at the origin and move 1 unit to the right , then move 3 units down . Point C is located in Quadrant IV .
Checkpoint Plot the point in the coordinate plane. Describe the
location of the point. 4. D(0, 3) Point D is located on the y-axis.
y 4
F (1, 2)
5. E(2, 4)
3
D (0, 3)
2 1
4 3 2
Point E is located in Quadrant III.
O
1
2
3
4 x
2 3
6. F(1, 2) E (2, 4)
4
Point F is located in Quadrant II.
Copyright © Holt McDougal. All rights reserved.
Chapter 1 • Pre-Algebra Notetaking Guide
19
Example 3
Making a Scatter Plot
The number of hours you spent studying for 5 different math tests and the score you got on each test is given in the table. Make a scatter plot of the data and describe any relationship you see. Hours studying
1
3
4
4
5
Test score
55
78
86
89
98
Solution 1. Write the data as ordered pairs. Let the x-coordinate represent the hours spent studying, and let the y-coordinate represent the test score: . 2. Plot the ordered pairs in a coordinate plane. You need only the first quadrant. 100 90 80 Test score
70 60 50 40 30 20 10 0
0 1 2 3 4 5 6 Hours studying
Notice that the points the hours spent studying
20
Chapter 1 • Notetaking Guide
from left to right. You can conclude as , your test scores
.
Copyright © Holt McDougal. All rights reserved.
Example 3
Making a Scatter Plot
The number of hours you spent studying for 5 different math tests and the score you got on each test is given in the table. Make a scatter plot of the data and describe any relationship you see. Hours studying
1
3
4
4
5
Test score
55
78
86
89
98
Solution 1. Write the data as ordered pairs. Let the x-coordinate represent the hours spent studying, and let the y-coordinate represent the test score: (1, 55), (3, 78), (4, 86), (4, 89), (5, 98) . 2. Plot the ordered pairs in a coordinate plane. You need only the first quadrant. 100 90 80 Test score
70 60 50 40 30 20 10 0
0 1 2 3 4 5 6 Hours studying
Notice that the points rise from left to right. You can conclude as the hours spent studying increases , your test scores increase .
20
Chapter 1 • Notetaking Guide
Copyright © Holt McDougal. All rights reserved.
