Name
Class
Date
Practice 12-1
Reflections
y
Use the figures to complete Exercises 1–5.
4
1. For figure IJKL, draw its reflection image in each line.
a. x-axis
b. y-axis
2
ⴚ6
ⴚ4
K
I
J
6 x
O
ⴚ2
ⴚ2
L
ⴚ4
2. In the diagram, C⬘D⬘E⬘F⬘ is the image of CDEF.
a. Name the images of ⬔C and ⬔F.
b. List the pairs of corresponding sides.
3. In the diagram, M⬘N⬘O⬘ is the image of MNO.
a. Name the images of ⬔M and ⬔N.
b. List the pairs of corresponding sides.
D
C
E
Cⴕ
Eⴕ
F
Fⴕ
N
Mⴕ
M
4. A⬘B⬘C⬘D⬘ is the image of ABCD.
a. Name the images of ⬔A and ⬔C.
b. List the pairs of corresponding sides.
Dⴕ
O
Oⴕ
Nⴕ
Aⴕ
B
A
C
Dⴕ
Bⴕ
© Pearson Education, Inc. All rights reserved.
D
5. For figure WXYZ, draw its reflection image in each line.
a. x-axis
b. y-axis
Cⴕ
y
4
W
ⴚ6
ⴚ4
ⴚ2
X
O
Z
ⴚ2
2
4
6 x
Y
ⴚ4
State whether each transformation appears to be an isometry. Explain.
6.
7.
8.
Given points T(2, 4), A(–3, –4), and B(0, –4), draw kTAB and its reflection
image in each line.
9. x-axis
10. y-axis
11. x = -3
12. y = 4
Geometry Chapter 12
Lesson 12-1 Practice
1
Name
Class
Date
Practice 12-3
Rotations
Regular octagon EIGHTSUP is divided into eight congruent triangles.
Find the image of each point or segment for the given rotation.
E
I
1. 45° rotation of G about Z
P
G
2. 225° rotation of U about Z
3. 315° rotation of E about Z
Z
4. 270° rotation of EI about Z
U
H
5. 135° rotation of S about Z
6. 360° rotation of ST about Z
S
T
Copy each figure and point P. Draw the image of each figure for the given
rotation about P. Label the vertices of each image.
7. 70°
8. 50°
9. 90°
O
T
P
P
N
P
S
U
© Pearson Education, Inc. All rights reserved.
Q
10. Rotate the hexagon 60° about point E, draw its image, and label the
vertices. Repeat this procedure three more times, rotating the original
figure 120°, 180°, and 240°.
M
N
L
O
E
Q
P
11. In Exercise 10, which vertex is closest to point E in all four figures?
S
P
Copy kPQR and point S. Then draw the image for the given composition
of rotations about point S.
12. 20° and then 70°
Q
13. 30° and then 30°
R
Geometry Chapter 12
Lesson 12-3 Practice
3
Chapter 12 Answers
10.
Practice 12-1
y
1a.
y
T
4
4
Lⴕ
2
ⴚ6 ⴚ4 ⴚ2
ⴚ6 ⴚ4 ⴚ2 O
ⴚ2 Iⴕ
ⴚ4
6 x
Kⴕ
Jⴕ
A
11.
y
1b.
2 4
ⴚ4
B Bⴕ
6 x
Aⴕ
y
Tⴕ
T
4
4
Kⴕ
Iⴕ
Jⴕ
O
ⴚ2
ⴚ6
Lⴕ
2
4
ⴚ8 ⴚ6 ⴚ4 ⴚ2
A ⴚ2
6 x
ⴚ4
2a. ⬔C⬘ and ⬔F⬘
2b. CD and C⬘D⬘, DE and D⬘E⬘,
3a. ⬔M⬘ and ⬔N⬘
EF and E⬘F⬘, CF and C⬘F⬘
3b. MN and M⬘N⬘, NO and N⬘O⬘, MO and M⬘O⬘
4a. ⬔A⬘ and ⬔C⬘
4b. AB and A⬘B⬘, BC and B⬘C⬘,
CD and C⬘D⬘, AD and A⬘D⬘
Bⴕ
Aⴕ ⴚ4
Aⴕ
y
Bⴕ
12.
Zⴕ
Yⴕ
ⴚ6 ⴚ4 ⴚ2
8 x
B
2
2 4
5b.
6
T, Tⴕ
4
Wⴕ
ⴚ4
4
6
4
2
2
10
y
5a.
© Pearson Education, Inc. All rights reserved.
Tⴕ
6x
ⴚ6 ⴚ4 ⴚ2
ⴚ2
Xⴕ
A
2
4
6x
ⴚ4 B
y
4
Xⴕ
ⴚ6 ⴚ4
Practice 12-2
Wⴕ
Yⴕ
ⴚ2
Zⴕ
4
6x
ⴚ4
6. No; the triangles are not the same size.
7. Yes; the
hexagons are the same shape and size.
8. Yes; the ovals
are the same shape and size.
9.
Aⴕ
4
y
T
Bⴕ
1. X
2. U
3. W
4. V
5. Z
6. Y
7. -2, -4
8. -2, -2
9. -3, -1
10. 4, -2
11. -5, 1
12. 2, 2
13. W⬘(-2, 2), X⬘(-1, 4),
Y⬘(3, 3), Z⬘(2, 1)
14. J⬘(-5, 0), K⬘(-3, 4), L⬘(-3, -2)
15. M⬘(3, -2), N⬘(6, -2), P⬘(7, -7), Q⬘(4, -6)
16. (x, y) S (x + 2, y + 3)
17. (x, y) S (x - 5,
y - 3)
18. (x, y) S (x + 2, y - 2)
19. 4.2, 11.2
20. 13, -13
21. 0, 0
22. 3, 3
23a. P⬘(-3, -1)
23b. P⬘(0, 8), N⬘(-5, 2), Q⬘(2, 3)
Practice 12-3
1. I
7.
2
2. I
A
2
4
S
Geometry Chapter 12
5. G
6. ST
P
6 x
ⴚ4 B T ⴕ
4. GH
Uⴕ
T
ⴚ6 ⴚ4 ⴚ2
ⴚ2
3. I
Tⴕ
U
Sⴕ
Answers
35
Chapter 12 Answers
(continued)
8.
Practice 12-4
1. I. D II. C III. B IV. A
3.
P
2. I. B II. A III. C IV. D
B B B
m
O
P Pⴕ
N
Q Oⴕ
4.
Qⴕ
C C
C
Nⴕ
10.
Oⴕ
Pⴕ
Nⴕ
Qⴕ
Mⴕ
Nⴕ
Lⴕ Lⴕ
Oⴕ
Lⴕ
Mⴕ
Nⴕ
Lⴕ
E
m
Pⴕ
5.
N
J
M
L
O
Q
Qⴕ
P
Nⴕ
Oⴕ
m
Mⴕ
Pⴕ
y
6.
4
Eⴕ
Sⴕ
11. L⬘
12.
Q'
ⴚ2
P'
S
R'
P
Q
m
J
J
Qⴕ
Oⴕ
Qⴕ
Mⴕ
Pⴕ
m
O
ⴚ2
2
4
Tⴕ
6 x
© Pearson Education, Inc. All rights reserved.
9.
Bⴕ
y
7.
10
Bⴕ
Tⴕ
8
R
13.
6
P'
Q'
4
S
Eⴕ
P
Sⴕ
2
R'
ⴚ4 ⴚ2 O
2
4 x
Q
y
8.
4
R
Eⴕ
Sⴕ
2
ⴚ2 O
ⴚ2
2
Tⴕ
4
6
8 x
Bⴕ
ⴚ4
36
Answers
Geometry Chapter 12
Name :
Score :
Teacher :
Date :
Rotations
ccw = counterclockwise
o
1) Rotation: 90 clockwise about the origin
Y^
5
< -5
-4
-3
-2
o
2) Rotation: 90 clockwise about the origin
Y^
5
4
4
3
3
2
2
1
1
-1
1
2
3
4
-1
-2
-3
-4
-5
V
>
5X
< -5
-4
-3
-2
...
-1
1
2
3
4
-1
. .
. .
>
5X
-2
-3
-4
-5
V
o
o
3) Rotation: 180 about the origin
Y^
5
4) Rotation: 180 about the origin
Y^
5
4
4
3
3
2
.
2
1
1
. .
< -5
-4
-3
-2
-1
1
2
3
4
>
5X
< -5
-4
-3
-2
-1
-2
-2
-3
-3
-4
-4
-5
-5
o
-3
-2
4
3
2
2
1
1
>
5X
.
.
1
2
3
4
>
5X
< -5
-4
-3
-2
-1
1
-1
-2
-2
-3
-3
-4
-4
-5
-5
V
4
o
3
-1
3
6) Rotation: 180 about the origin
Y^
5
4
-1
2
V
5) Rotation: 90 clockwise about the origin
Y^
5
-4
1
-1
V
< -5
.
.
-1
. .
. .
.
2
.
3
4
>
5X
V
Math-Aids.Com
Name :
Score :
Teacher :
Date :
Rotations
ccw = counterclockwise
o
1) Rotation: 90 clockwise about the origin
Y^
5
< -5
. ..
.
-4
-3
-2
o
2) Rotation: 90 clockwise about the origin
Y^
5
4
4
3
3
2
2
1
1
-1
1
2
3
4
-1
-2
-3
-4
-5
V
>
5X
< -5
-4
-3
-2
...
...
-1
1
-1
. .
. .
-2
-3
2
3
4
>
5X
-4
-5
V
o
o
3) Rotation: 180 about the origin
Y^
5
4) Rotation: 180 about the origin
Y^
5
4
4
3
3
2
.
.
2
1
1
. .
< -5
-4
-3
-2
-1
1
2
3
4
-1
>
5X
< -5
-4
-3
-4
-2
-1
.
. .
-2
-3
.
3
2
-1
1
-1
-4
-5
V
4
>
5X
-3
-4
o
2
3
4
.
4
.
3
2
>
5X
< -5
-4
.
-3
1
-2
-1
1
.
-1
-2
-3
3
6) Rotation: 180 about the origin
Y^
5
. .
. .
4
1
-2
2
V
o
-3
1
-5
5) Rotation: 90 clockwise about the origin
Y^
5
-4
.
-2
V
< -5
.
.
-1
-5
. .
. .
.
2
.
3
4
>
5X
-2
.
-3
-4
-5
V
Math-Aids.Com