NAME ______________________________________________ DATE ____________ PERIOD _____

2-6 Study Guide and Intervention

The Coordinate System

y
The x-coordinate is negative. 4 Both coordinates are positive.
The y-coordinate is positive. 3
( , ) 2 ( , )
1
O
4 3 2 1 1 2 3 4x
1
2
( , ) 3 ( , ) The x-coordinate is positive.
Both coordinates are negative. 4 The y-coordinate is negative.

Example Graph and label each point on a coordinate plane. Name the
quadrant in which each point lies.

a. M(⫺2, 5) 5
y
M 4
Start at the origin. Move 2 units left.
3
Then move 5 units up and draw a dot. 2
1
O
Point M(⫺2, 5) is in Quadrant II. x
4 3 2 1 1 2 3
1
b. N(4, ⫺4) 2
3
Start at the origin. Move 4 units right. 4
N

Then move 4 units down and draw a dot.

Point N(4, ⫺4) is in Quadrant IV.

Exercises

Graph and label each point on the coordinate plane.

Name the quadrant in which each point is located.

1. A(2, 6) I 2. B(⫺1, 4) II 8
y

7
3. C(0, ⫺5) none 4. D(⫺4, ⫺3) III 6
A
5
G B 4
5. E(2, 0) none 6. F(3, ⫺2) IV I
3
7. G(⫺4, 4) II 8. H(2, ⫺5) IV 2
1
O E
9. I(6, 3) I 10. J(⫺5, ⫺8) III 8 7 6 5 4 3 2 1
1
1 2 3 4 5 6 7 8x
F
2
L D
11. K(3, ⫺5) IV 12. L(⫺7, ⫺3) III 3
4
C H K
5
6
7
J
8

© Glencoe/McGraw-Hill 82 Glencoe Pre-Algebra

 NAME ______________________________________________ DATE ____________ PERIOD _____

2-6 Skills Practice

The Coordinate System

Lesson 2-6
Name the ordered pair for each point graphed at the right.

1. A (⫺2, 2) 2. B (3, ⫺7) 7

y

6
I J D
5
4
3. C (⫺4, 0) 4. D (3, 5) 3
A E
2
1
C O H
5. E (4, 2) 6. F (⫺6, ⫺3) 7 6 5 4 3 2 1 1 2 3 4 5 6 7x
1
2
F G
3
7. G (2, ⫺3) 8. H (5, 1) 4
5
6
B
7
9. I (⫺7, 6) 10. J (⫺5, 5)

Graph and label each point on the coordinate plane. Name the quadrant in which
each point is located.
y
11. K (1, 0) none 12. L (0, 2) none 7
T
6
5
U M
4
13. M (⫺2, 4) II 14. N (⫺5, ⫺4) III 3
L
2
1
O K
15. P (6, ⫺2) IV 16. Q (7, ⫺6) IV 7 6 5 4 3 2 1
1
1 2 3 4 5 6 7x
2
P
3
N
17. R (⫺3, ⫺4) III 18. S (4, ⫺7) IV R
4
5
Q
6
S
7
19. T (3, 6) I 20. U (⫺7, 4) II
21. ALGEBRA Make a table of values and graph six sets of ordered pairs for the
equation y ⫽ x ⫺ 4. Describe the graph.
y
y⫽x⫺4 1
O
The points are along a line
4 3 2 1
1
1 2 3 4x slanting up to the right,
x y (x, y)
2 crossing the y-axis at ⫺4
3 ⫺1 (3, ⫺1) 3 and the x-axis at 4.
4
5
2 ⫺2 (2, ⫺2) 6
7
1 ⫺3 (1, ⫺3)
0 ⫺4 (0, ⫺4)
⫺1 ⫺5 (⫺1, ⫺5)
⫺2 ⫺6 (⫺2,⫺6)

© Glencoe/McGraw-Hill 83 Glencoe Pre-Algebra

 NAME ______________________________________________ DATE ____________ PERIOD _____

2-6 Practice
The Coordinate System

Graph and label each point on the coordinate plane. Name the quadrant in which
each point is located.
y
14
J
12
1. A (8, 6) I 2. B (⫺8, 6) II 10
8
B A
3. C (⫺4, ⫺11) III 4. D (3, ⫺6) IV 6
4
2
F O E
5. E (9, 0) none 6. F (⫺4, 1) II 14 10 6 2 2 4 6 8 10 12 14x
2
I
4
D
7. G (⫺10, ⫺10) III 8. H (0, ⫺8) none 6
H
8
G
10
C
9. I (6, ⫺2) IV 10. J (2, 13) I 12
14

11. ALGEBRA Make a table of values and graph six sets of ordered pairs for the
equation y ⫽ 5 ⫺ x. Describe the graph.

y⫽5⫺x y The points are along a line

7
6
slanting down to the right,
x y (x, y) 5 crossing the y-axis at 5 and
3 2 (3, 2) 4 the x-axis at 5.
3
2
2 3 (2, 3) 1
O
(1, 4) 4 3 2 1 1 2 3 4x
1 4 1

0 5 (0, 5)
⫺1 6 (⫺1, 6)
⫺2 7 (⫺2, 7)

12. GEOMETRY On the coordinate plane, draw a rectangle ABCD with vertices at
A(1, 4), B(5, 4), C(5, 1), and D(1, 1). Then graph and describe the new rectangle
formed when you subtract 3 from each coordinate of the vertices in rectangle ABCD.

y
The new rectangle
5
A B is the same size as
4
3 rectangle ABCD and
A'
2
D B' C
is shifted to the left
1
O 3 units and down 3 units,
4 3 2 1 1 2 3 4 5x with vertices at (⫺2, 1),
1
D' C'
2 (2, 1), (2, ⫺2), and (⫺2, ⫺2).
3

© Glencoe/McGraw-Hill 84 Glencoe Pre-Algebra

©
NAME ______________________________________________ DATE ____________ PERIOD _____ NAME ______________________________________________ DATE ____________ PERIOD _____

2-5 Enrichment 2-6 Study Guide and Intervention

The Coordinate System

Cross-Number Puzzle y
The x-coordinate is negative. 4 Both coordinates are positive.
Use the clues below to complete the following cross-number puzzle. Any negative The y-coordinate is positive. 3

Glencoe/McGraw-Hill
signs should be placed in the same box as the first digit of the integer. ( , ) 2 ( , )
1
O
4 3 2 1 1 2 3 4x
1
ACROSS 1 2 3 4
2
1 2 4 2 ( , ) 3 ( , ) The x-coordinate is positive.
1. 23 ?(2 54) Both coordinates are negative. 4 The y-coordinate is negative.
5 6 7 8 9
5. 2 56 2 15 7 1 3 0 3 3 3 6
10 11 12 Example
7. 2 4283 1 7316
4 0 4 4 5 6 8 0 Graph and label each point on a coordinate plane. Name the
quadrant in which each point lies.
8. 46.8 4 (2 1.3)
8 8
10. 2 3840 4 (2 96) a. M( 2, 5) y
13 14 15 16 5
M 4
11. 2 1.6 ?(2 2785) 7 2 1 2 4 Start at the origin. Move 2 units left.
3
17 18 19 20 Then move 5 units up and draw a dot. 2
12. 91.5 1 (2 11.5) 1
7 5 3 9 0 5 8 O
Point M(2 2, 5) is in Quadrant II. x
13. 2 42 2 679 4 3 2 1 1 2 3
21 22 23 24 25 1
1 9 2 4 7 0 5 8 b. N(4, 4) 2
15. 50 ?(2 0.48) 3
26 27 28 Start at the origin. Move 4 units right. N
4
18. 2 53,000 ?(2 0.001) 1 8 9 6 4 0 1 6 Then move 4 units down and draw a dot.

A14
19. 2 181 ?5 29
6 0 5 0 Point N(4, 2 4) is in Quadrant IV.
21. 2 42 1 61
23. 10 ?(2 13) ?(2 19) DOWN Exercises
25. 26.1 4 (2 0.45) 1. 2 718 1 584 14. 2 832 ?(2 28)
Graph and label each point on the coordinate plane.
26. 2 750 ?(2 0.024) 2. 2 0.8 ?(2 255) 15. 2 40 ?(2 20) ?(2 25) Name the quadrant in which each point is located.
27. 2 38.56 4 (2 0.004) 3. 198 2 (2 237) 16. 2 9 ?(2 5) 1. A(2, 6) I 2. B(2 1, 4) II y
8
28. 2 38 2 (2 54) 7
4. 2 118 4 (2 0.5) 17. 2 79 ?3 ?3 A
3. C(0, 2 5) none 4. D(2 4, 2 3) III 6
Answers (Lessons 2-5 and 2-6)

29. 11,260 1 (2 5210) 5

5. 2 2 ?(2 22) ?(2 17) 19. 2 13,406 1 3661 G B 4
5. E(2, 0) none 6. F(3, 2 2) IV I
3
6. 2 1000 4 (2 100 20. 2 649 1 1535 2
7. G(2 4, 4) II 8. H(2, 2 5) IV
1
O E
8. 2 6.46 4 0.17 22. 46 2 (2 52) 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8x
9. I(6, 3) I 10. J(2 5, 2 8) III 1
F
9. 1547 1 (2 939) 24. 2 10 ?(2 46) 2
L D
11. K(3, 2 5) IV 12. L(2 7, 2 3) III 3
13. 2 5000 ?0.015 4
25. 2 0.663 4 0.013 C H K
5
6
7
J
8
Lesson 2-5

© Glencoe/McGraw-Hill 81 Glencoe Pre-Algebra © Glencoe/McGraw-Hill 82 Glencoe Pre-Algebra

Glencoe Pre-Algebra
©
NAME ______________________________________________ DATE ____________ PERIOD _____ NAME ______________________________________________ DATE ____________ PERIOD _____

2-6 Skills Practice 2-6 Practice

The Coordinate System The Coordinate System

Name the ordered pair for each point graphed at the right. Graph and label each point on the coordinate plane. Name the quadrant in which
y
each point is located.
1. A ( 2, 2) 2. B (3, 7) y
7 14
J

Glencoe/McGraw-Hill
6 12
I J D 1. A (8, 6) I 2. B (2 8, 6) II
5 10
4

Lesson 2-6
3. C ( 4, 0) 4. D (3, 5) 8
3 B A
A E 3. C (2 4, 2 11) III 4. D (3, 2 6) IV 6
2 4
1 2
C O H F O E
5. E (4, 2) 6. F ( 6, 3) 7 6 5 4 3 2 1 1 2 3 4 5 6 7x 5. E (9, 0) none 6. F (2 4, 1) II 14 10 6 2 2 4 6 8 10 12 14x
1 2
2 I
F G 4
3 D
7. G (2 10, 2 10) III 8. H (0, 2 8) none 6
7. G (2, 3) 8. H (5, 1) 4 H
8
5 G
10
6 C
B 9. I (6, 2 2) IV 10. J (2, 13) I 12
7 14
9. I ( 7, 6) 10. J ( 5, 5)

11. ALGEBRA Make a table of values and graph six sets of ordered pairs for the
Graph and label each point on the coordinate plane. Name the quadrant in which
each point is located. equation y 5 5 2 x. Describe the graph.
y
11. K (1, 0) none 12. L (0, 2) none 7 y The points are along a line
T y 5 x 7
6
5 6 slanting down to the right,
U M x y (x, y ) 5
4 crossing the y-axis at 5 and
13. M (2 2, 4) II 14. N (2 5, 2 4) III 3 4
L the x-axis at 5.
2 3 2 (3, 2) 3

A15
1 2
O K
7 6 5 4 3 2 1 1 2 3 4 5 6 7x 2 3 (2, 3) 1
15. P (6, 2 2) IV 16. Q (7, 2 6) IV 1 O
2 4 3 2 1 1 2 3 4x
P 1 4 (1, 4) 1
3
N 4
17. R (2 3, 2 4) III 18. S (4, 2 7) IV R 0 5 (0, 5)
5
Q
6
S 1 6 ( 1, 6)
7
19. T (3, 6) I 20. U (2 7, 4) II
Answers (Lesson 2-6)

2 7 ( 2, 7)
21. ALGEBRA Make a table of values and graph six sets of ordered pairs for the
equation y 5 x 2 4. Describe the graph.
y 12. GEOMETRY On the coordinate plane, draw a rectangle ABCD with vertices at
y x 4 1 The points are along a line
O A(1, 4), B(5, 4), C(5, 1), and D(1, 1). Then graph and describe the new rectangle
4 3 2 1 1 2 3 4x slanting up to the right,
1 formed when you subtract 3 from each coordinate of the vertices in rectangle ABCD.
x y (x, y) crossing the y-axis at 4
2
3 and the x-axis at 4.
3 1 (3, 1) 4 y
The new rectangle
5 5 is the same size as
A B
2 2 (2, 2) 6 4
7 3 rectangle ABCD and
1 3 (1, 3) 2 is shifted to the left
A' D B' C
1
O 3 units and down 3 units,
0 4 (0, 4) 4 3 2 1 1 2 3 4 5x
1 with vertices at ( 2, 1),
D' C'
1 5 ( 1, 5) 2 (2, 1), (2, 2), and ( 2, 2).
3
2 6 ( 2, 6)

© Glencoe/McGraw-Hill 83 Glencoe Pre-Algebra © Glencoe/McGraw-Hill 84 Glencoe Pre-Algebra

Glencoe Pre-Algebra
Answers