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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
GeometryChapter Resource Book9-64
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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”
GeometryChapter Resource Book 9-65
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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
9.5