Problem Solving 12-5 - Parkland School District

Name Date Class 

LESSON 

12-5 

Problem Solving 

Graphing Rotations 

Write the correct answer. 

1. Graph points A(8, 2), B(8, 7), 

C(5, 7), and D(5, 2). Then join the 

points to form rectangle ABCD. 

8 

4 

y 

2. Rotate ABCD 180° counterclockwise 

about the origin. What are the 

coordinates of the rotated rectangle 

8 

4 

O 4 8 

x 

4 

8 

3. Reflect ABCD across the y-axis. 

Then reflect the reflected ABCD 

across the x-axis. What are the 

coordinates of the double-reflected 

rectangle 

4. What conclusion can you make about 

the relationship between a double 

reflection of a figure over both axes 

and a 180° rotation of that figure 

about the origin 

Circle the letter of the correct answer. 

5. The vertices of triangle ABC are 

A(5, 3), B(10, 7), and C(1, 7). 

What are the coordinates of the 

vertices if it is rotated 90° 

counterclockwise about the origin 

A A'(5, 3), B'(10, 7), 

C'(1, 7) 

B A'(5, 3), B'(10, 3), C'(1, 7) 

C A'(3, 5), B'(7, 10), C'(7, 1) 

D A'(3, 5), B'(7, 10), C'(7, 1) 

6. How do you find the coordinates of the 

vertices of a figure when it is rotated 

180° clockwise about the origin 

F Change the sign of both 

coordinates. 

G Change the sign of the 

x-coordinate and reverse 

the coordinates. 

H Change the sign of the 

y-coordinate and reverse 


J Change the sign of 

the x-coordinate. 

Copyright © by Holt, Rinehart and Winston. 

51 Holt Middle School Math Course 1 

All rights reserved.

LESSON 


Problem Solving 

Graphing Rotations 

Write the correct answer. 

1. Graph points A(8, 2), B(8, 7), 

C(5, 7), and D(5, 2). Then join the 

points to form rectangle ABCD. 

Check students’ graphs. 

2. Rotate ABCD 180° counterclockwise 

about the origin. What are the 

coordinates of the rotated rectangle 

Check students’ graphs; 

A'(8, 2); B'(8, 7); 

C'(5, 7); D'(5, 2) 

3. Reflect ABCD across the y-axis. 

Then reflect the reflected ABCD 

across the x-axis. What are the 

coordinates of the double-reflected 

rectangle 

Check students’ graphs; 

A''(8, 2);B''(8, 7); 

C''(5, 7); D''(5, 2) 

Circle the letter of the correct answer. 

5. The vertices of triangle ABC are 

A(5, 3), B(10, 7), and C(1, 7). 

What are the coordinates of the 

vertices if it is rotated 90° 

counterclockwise about the origin 

A A'(5, 3), B'(10, 7), 

C'(1, 7) 

B A'(5, 3), B'(10, 3), C'(1, 7) 

C A'(3, 5), B'(7, 10), C'(7, 1) 

D A'(3, 5), B'(7, 10), C'(7, 1) 

B 

A 

8 

C 

8 

4 

D 

x 

4 O 4 8 

D' 

A' 

4 

8 

4. What conclusion can you make about 

the relationship between a double 

reflection of a figure over both axes 

and a 180° rotation of that figure 

about the origin 

They are the same 

transformation of the figure. 

6. How do you find the coordinates of the 

vertices of a figure when it is rotated 

180° clockwise about the origin 

F Change the sign of both 

coordinates. 

G Change the sign of the 

x-coordinate and reverse 


H Change the sign of the 

y-coordinate and reverse 


J Change the sign of 

the x-coordinate. 

y 

C' 

B' 

LESSON 


Puzzles, Twisters & Teasers 

Which Way Did IT Go 

Compare the first figure to the second figure in each pair. 

Decide how the figure has been rotated: 90, 180, or 360. 

Circle the correct answer. Use the letters to solve the riddle. 

1. WXYZ W'X'Y'Z' D 90° rotation 

W (0, 0) W' (0, 0) 

X (3, 1) X' (3, 1) E 180° rotation 

Y (2, 3) Y' (2, 3) 

Z (1, 1) Z' (1, 1) C 360° rotation 

2. DEFG D'E'F'G' A 90° rotation 

D (6, 4) D' (4, 6) 

E (2, 4) E' (4, 2) Y 180° rotation 

F (0, 0) F' (0, 0) 

G (8, 0) G' (0, 8) O 360° rotation 

3. NOPQ N'O'P'Q' R 90° rotation 

N (0, 0) N' (0, 0) 

O (2, 4.5) O' (2, 4.5) K 180° rotation 

P (4.5, 6) P' (4.5, 6) 

Q (4.5, 1.5) Q' (4.5, 1.5) W 360° rotation 

4. LMN L'M'N' I 90° rotation 

L (1, 4) L' (1, 4) 

M (5, 3) M' (5, 3) U 180° rotation 

N (3, 1) N' (3, 1) 

E 360° rotation 

5. JKLM J'K'L'M' L 90° rotation 

J (0, 0) J' (0, 0) 

K (1, 4) K' (4, 1) G 180° rotation 

L (2, 4) L' (4, 2) 

M (4, 1) M' (1, 4) M 360° rotation 

What vegetable was not welcome on the Titanic A LEEK 

y 

4 Y' 

Z 

W X' x 

4 O 4 

X Z' 

Y 4 

y 

G' 

8 

D' 

D E 

4 

E' 

G 

x 

8 4 O F 4 8 

y 

P 

O 

4 

N Q x 

4 O 4 

Q' 

4 

P' O' 

y 

LL' 

4 M M' 

N N' x 

4 O 4 

y 

K L 

4 

N J M x 

4 O 4K' 

L' 

4 

M' 



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LESSON 


Exploration Recording Sheet 

Stretching and Shrinking 

You can stretch the triangle in the coordinate plane. 

3 

1. Label the height and width of the triangle. 

2. Create a new triangle by multiplying the dimensions 

by 2. 

3. Explain how the height and width of the triangle 

changed after the dimensions were multiplied by 2. 

The height and width each doubled. 

Think and Discuss 

4. Discuss real-world applications of stretches. 

3 

Possible answer: lengthening a pattern 

6 

5. Explain how many times the original triangle fits into the 

triangle you drew in Exercise 2. 

4 times 

6 

LESSON 


Practice A 

Stretching and Shrinking 

Write the dimensions of each part 

of the figure. Stretch the figure as 

stated and give the new dimensions 

of each part. 

1. Original dimensions: 

horizontal: 2 squares 

and vertical: 3 squares 

2. Increase the horizontal dimension by 

a factor of 2. 



Write the dimensions of each part 

of the figure. Shrink the figure as 

stated and give the new dimensions 

of each part. 

4. Original dimensions: 



3. Increase the vertical dimension by a 

factor of 4. 


and vertical: 12 squares 

5. Decrease the vertical dimension by 6. Decrease the horizontal dimension 

multiplying by 1 3 . 

by a multiplying by 1 2 . 



and vertical: 1 3 square and vertical: 1 square 

7. If you decrease the vertical dimension of the photograph 

by a factor of 2, what are its new dimensions 

6 inches wide and 5 inches tall 

8. Using the photograph in Exercise 7. If you increase its 

horizontal dimension by a factor of 2, what are its new 

dimensions 

12 inches wide and 10 inches tall 

10 in. 

6 in. 









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Problem Solving 12-5 - Parkland School District

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