ame: ________________________ Class: ___________________ Date: __________
Transformations
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1. Name the image of S under a reflection in line m.
a.
b.
c.
d.
b.
c.
T
V
S
W
Graph each figure and its image under the given
translation.
2. ∆EFG with vertices
E(−2, − 3), F(−3, − 2), G(−1, − 1) under the
translation left three units and down two units
a.
d.
1
ID: A
ame: ________________________
ID: A
3. ∆XYZ with endpoints
X(−2, − 2), Y(−4, − 4), Z(−3, − 4) under the
translation (x, y) → (x + 2, y − 2)
c.
a.
d.
b.
2
ame: ________________________
ID: A
In each figure, a Ä b . Determine whether the third figure is a translation image of the first figure. Write yes or no.
Explain your answer.
4.
a.
b.
c.
d.
Yes; it is one reflection after another with respect to the two parallel lines.
No; it is a reflection followed by a translation.
No; it is a reflection followed by a rotation.
No; it is one reflection after another with respect to the two parallel lines.
3
ame: ________________________
ID: A
Copy parallelogram ABCD.
Find the endpoints of the image of AB.
6. Reflect AB over the x-axis and rotate 90° about the
origin.
5. Rotate the parallelogram 90° counterclockwise
about point Q.
a.
b.
a.
b.
c.
d.
A”(4, –4), B”(2, –2)
A”(–4, –4), B”(–2, –2)
A”(–4, 4), B”(–2, 2)
A”(–2, 2), B”(–4, 4)
Determine how many lines of symmetry each object
has. Then determine whether each object has point
symmetry.
c.
7.
d.
a.
b.
c.
d.
4
6; no
6; yes
5; no
5; yes
ame: ________________________
ID: A
8. What is the order of the symmetry of the pizza
shown below?
a.
b.
c.
d.
10.
8
7
6
4
a. 1; reduction
b. 1; congruence
c. 1; enlargement
d. 1; reflection
11. The rule for this transformation of
A′B ′C ′ is _________ .
Determine the scale factor for each dilation.
Determine whether the dilation is an enlargement,
reduction, or congruence transformation.
9.
a.
b.
c.
3; enlargement
3; reduction
1
; enlargement
3
d.
1
3
a.
b.
c.
d.
; reduction
5
(x, y) → (x – 9, y – 2)
(x, y) → (x + 9, y + 2)
(x, y) → (x – 9, y + 2)
(x, y) → (x + 9, y – 2)
ABC onto
ame: ________________________
12.
ID: A
15. The transformation ÊÁË x, y ˜ˆ¯ → ÁÊË −x, − y ˜ˆ¯ is applied
to the figure below. Graph the image of the figure
under this transformation.
What are the coordinates of the vertices when the
figure is reflected in line m?
a. W ′ (4, –3), X ′ (1, 4), Y ′ (–2, 0)
b. W ′ (–3, 4), X ′ (4, 1), Y ′ (0, –2)
c. W ′ (2, –3), X ′ (1, –4), Y ′ (–4, 0)
d. W ′ (2, 3), X ′ (–1, –4), Y ′ (–4, 0)
13. A reflection is always ________.
a. a rotation
b. a translation
c. an isometry
d. reflexive
14. Use the graph below to complete the sentence.
Figure A′B ′C ′D ′ is the image of figure ABCD
under a rotation _______
a.
b.
c.
d.
270° counterclockwise about the origin.
180° about the origin.
90° counterclockwise about the origin.
270° clockwise about the origin.
6
ame: ________________________
ID: A
16. Which glide reflection could map triangle ABC to
triangle A′B ′C ′?
a.
b.
a.
b.
c.
c.
d.
Translation: ÊÁË x, y ˆ˜¯ →
Reflection: in y = 0
Translation: ÊÁË x, y ˆ˜¯ →
7
ÊÁ x, y − 3 ˆ˜
Ë
¯
Reflection: in y = 0
Translation: ÊÁË x, y ˆ˜¯ → ÊÁË x − 3, y ˆ˜¯
Reflection: in x = 0
Translation: ÊÁË x, y ˆ˜¯ → ÊÁË x, y − 3 ˆ˜¯
Reflection: in x = 0
d.
ÊÁ x − 3, y ˆ˜
Ë
¯
ame: ________________________
ID: A
18. The hexagon shown below is equiangular. How
many lines of symmetry does it have?
Graph DEF with vertices
D ÊÁË 0, 3 ˆ˜¯ , E ÊÁË 4, 3 ˆ˜¯ , and F ÊÁË 0, 7 ˆ˜¯ . Then graph its
image after the given transformation.
17. Rotate 180°. Then translate using
ÊÁ x, y ˆ˜ → ÊÁ x − 1, y − 1 ˆ˜ .
Ë
¯
Ë
¯
a.
a. 2
b. 1
c. 3
d. 6
19. Which figure has rotational symmetry
for an angle of rotation of 240°?
b.
c.
d.
8
ame: ________________________
ID: A
a.
b.
c.
d.
9
ame: ________________________
ID: A
Short Answer
20. Graph the triangle whose vertices have the
coordinates given below. Then draw its reflection
in the x-axis.
(–7, 2), (–2, 2), (–6, 7)
21. The points in a coordinate plane are reflected in the
y-axis. In general, every point (x, y) is mapped onto
what point?
22. Find the coordinates of the image of a triangle with
vertices A(0, 2), B(–2, 0), and C(6, –4) for a
rotation of 90° counterclockwise about the origin.
Draw the image of the given figure after a
dilation with center O and the given scale factor.
23. scale factor:
1
2
Tell what type of transformation is described.
24. The coordinates of the image are four times the
corresponding coordinates of the original.
10
ID: A
Transformations
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
D
A
B
A
B
A
D
A
A
B
C
A
C
A
D
D
C
A
D
SHORT ASWER
20.
21. (–x, y)
22. A′( − 2, 0), B ′(0, − 2), C ′(4, 6)
1
ID: A
23.
24. dilation
2