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Practice BFor use with the lesson “Apply Compositions of Transformations”

The endpoints of } CD are C(1, 2) and D(5, 4). Graph the image of } CD after the glide reflection.

1. Translation: (x, y) → (x 2 4, y) 2. Translation: (x, y) → (x, y 1 2) Reflection: in the x-axis Reflection: in y 5 x

x

y

1

1

x

y

1

1

The vertices of n ABC are A(3, 1), B(1, 5), and C(5, 3). Graph the image of n ABC after a composition of the transformations in the order they are listed.

3. Translation: (x, y) → (x 1 3, y 2 5) 4. Translation: (x, y) → (x 2 6, y 1 1) Reflection: in the y-axis Rotation: 908 about the origin

x

y

1

21

x

y 1

21

Graph } F 0G 0 after a composition of the transformations in the order they are listed. Then perform the transformations in reverse order. Does the order affect the final image } F 0G 0 ?

5. F(4, 24), G(1, 22) 6. F(21, 23), G(24, 22)

Rotation: 908 about the origin Reflection: in the line x 5 1 Reflection: in the y-axis Translation: (x, y) → (x 1 2, y 1 10)

x

y

1

1

x

y

1

1

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Describe the composition of transformations.

7.

x

y

1

5

A A99

A9 B9

C9 D9

D99

C99

B99

B

C D

8.

x

y

1

1

A

A99

A9

B9

C9

B99

C99 B

C

In the diagram, k i m, } AB is reflected in line k, and }

A9B9 is reflected in line m.

9. A translation maps }

AB onto which segment?

A

A9

A99

B

B9

B99

k

m

10. Which lines are perpendicular to @###$ BB0 ?

11. Name two segments parallel to }

AA0 .

12. If the distance between k and m is 2.7 centimeters, what is the length of

} AA0 ?

13. Is the distance from A9 to m the same as the distance from A0 to m? Explain.

Find the angle of rotation that maps A onto A0.

14.

A

A9

A99

k

m

608

15.

AA9

A99

k

m

458

16. Stenciling a Border The border pattern below was made with a stencil. Describe how the border was created using one stencil four times.

Practice B continuedFor use with the lesson “Apply Compositions of Transformations”

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Practice Level B

1.

x

y

1

1

C99(23, 22)

D99(1, 24)

2.

x

y

1

1 C99(4, 1)

D99(6, 5)

3.

x

y

1

21

C99(28, 22)

B99(24, 0)

A99(26, 24)

4.

x

y 1

21 C99(24, 21)

A99(22, 23)B99(26, 25)

5.

x

y

1

21

F99(24, 4)

F99(4, 24)

G99(22, 1)G99(2, 21)

reflection then

rotation

rotation then

reflection

6.

x

y

1

1

F99(1, 7) F99(5, 7)

G99(4, 8) G99(8, 8)

translationthen

reflection

reflectionthen

translation

yes yes

7. Reflection in y 5 1 }

2 , followed by 2708 rotation

about (1, 23). 8. 2708 rotation about (22, 21), followed by the translation (x, y) → (x 1 5, y 2 2).

9. }

A0B0 10. k and m 11. }

BB9 , }

BB0 12. 5.4 cm

13. yes; definition of reflection 14. 1208 15. 908

16. After each part was painted, the stencil was moved through a glide reflection (reflection in a horizontal line and translation to the right) to paint the next part.

Practice Level C

1. A9(23, 23), B9(25, 1), C9(29, 21)

2. A9(5, 1), B9(7, 5), C9(11, 3) 3. A9(3, 21), B9(21, 1), C9(1, 5) 4. A9(26, 27), B9(24, 23), C9(0, 25) 5. A9(3, 1), B9(21, 21), C9(1, 25)

6.

x

y 4

1

A0(3, 0)

C 0(1, 23)

B 0(21, 2)

7.

x

y

1

1

A0(0, 3)

C 0(3, 5)

B 0(22, 7)

8.

x

y

1

F 0(1, 0)

G 0(3, 3)F 0(23, 2)

G 0(25, 21)

rotationthen reflection

reflectionthen rotation

; yes

9.

x

y 2

2

F 0(3, 27)

F 0(6, 24)

G 0(0, 210)

G 0(3, 27)

translationthen reflection

reflectionthen translation

; yes

10. Translation (x, y) → (x 1 5, y 2 4) followed by reflection in x-axis. 11. Rotation of 2708 about (0, 2) followed by translation (x, y) → (x, y 1 4).

12. }

N0P0 13. e and h 14. }

PP9 , }

PP0

15. 2.4 cm 16. yes; definition of reflection

17. 1408 18. 1988 19. yes; ⟨0.025, 0⟩ 20. no

Study Guide

1. A0(24, 22), B0(27, 21), C0(28, 23)

2. Reflection: the x-axis, Translation: (x, y) → (x 1 11, y)

3. Yes, the resulting segment }

R0S0 is different if the order of transformations is different.

x

y

2

2

R

S

R 0

S 0

R9

S9

4. They are opposite sides of a parallelogram.

5. translation 6. 30 units, }

HH9 ⊥ @##$ k

Real-Life Application

1. translation, a reflection over a vertical line, and a 908 rotation counterclockwise

2. translation and a reflection over a horizontal line 3. translation and a 908 rotation counterclockwise 4. translation, a reflection over a vertical line, and a 908 rotation clockwise

Challenge Practice

1. (x, y) → (x 2 14, y 2 8)

2. (x, y) → (x 2 21, y 2 12)

Lesson Apply Compositions of Transformations, continued

GeometryChapter Resource BookA40

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