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Chapter 6 Review
For #1-5: Triangle PQR has vertices as shown.
1. If the figure is translated 6 units down, what are the coordinates of
?
2. If the figure is translated 1 unit left and 2 units down, what are the coordinates of
?
3. If the figure is rotated 270° clockwise about the origin, what are the coordinates of
?
4. If the figure is reflected over the y-axis, what are the coordinates of
?
5. If the figure is dilated using a scale factor of 3, what are the coordinates of
?
6. Triangle LMN has vertices L(–1, 4), M(–2, 4), and N(–1, –1). What are the coordinates of the image
of point M after a dilation with a scale factor of 3?
7. Triangle RST has vertices R(–1, 1), S(3, 1), and T(3, –4). What are the coordinates of the image of
RST after a translation 4 units to the left and 2 units down?
8. Quadrilateral WXYZ has vertices W(–3, 4), X(–3, 1), Y(2, 1), and Z(2, 4). What are the coordinates of
the image of point W after a reflection across the y-axis?
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9. Triangle PQR has vertices P(6, 5), Q(6, 10), and R(0, 5). What are the coordinates of the image of
point P after the triangle is rotated 180° clockwise about the origin?
10. The graph shows segment
is a dilation of segment MN. What is the scale factor of the dilation?
(Use one of the coordinates to calculate)
11. A projector transforms the image on a computer screen so that it is dilated by a scale factor of
7
. If
2
the original image on the screen is 10 inches wide, find the new width in inches after it is projected
on the wall.
12. The triangle
NLM.
shown was reflected over the x-axis. Find the original coordinates of the triangle
13. In the figure below,
is a dilation of
it as an enlargement or a reduction.
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XYZ. Find the scale factor of the dilation, and classify
Triangle PQR is rotated 90° clockwise about the origin. The vertices of the triangle are P(3, 1),
Q(1, 4), and R(2, –5).
14. Find the coordinates of P’, Q’ and R’
15. True or false: m<P is greater than the m<P’. Explain why you chose your answer.
16. True or False: When ∆PQR is rotated 90° clockwise about the origin the orientation is changed.
Explain why you chose your answer.
17. The area of ∆PQR is 15 in2, what is the area of ∆P’Q’R’?
18. The point
(4, –5) is the result of a translation of 4 units left and 2 units up. Use translation notation
to describe the translation.
19. What are the coordinates of the image of A(2, 5) after it is rotated 180 clockwise about the origin?
QRSTUV to Q’R’S’T’U’V’
U
A. reflection over the x-axis and translation 8 units right
20. Which sequence of transformations takes
B. reflection over the y-axis and translation 2 units down
C. 180° rotation about the origin and translation 4 right
D. translation 4 units left and 90° rotation about the origin
21. If ∆ABC is rotated 90° clockwise about the origin,
What will be the new coordinates of vertex B?
A. (−1, −4)
B. (1, 4)
C. (4, 1)
D. (4, −1)
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U
22. Figure Q was the result of a sequence of transformations on
figure P, both shown below. Which sequence of transformations
could take figure P to figure Q?
A. reflection over the x-axis and translation 7 units right
B. reflection over the y-axis and translation 3 units down
C. translation 1 unit right and 180° rotation about the origin
D. translation 4 units right and 180° rotation about the origin
23. Figure 1 can be transformed to create Figure 2 using a single
transformation. Which transformation can be used to do this?
A. dilation
B. rotation
C. reflection
D. translation
24. The circle shown below is centered at the origin and passes through point P located
at (2,0). The circle is dilated with the center of dilation at the origin
and a scale factor of 0.5 and then translated up 3 units.
What are the coordinates of the image of point P after
this transformation?
A. (4, 3)
B. (1, 3)
C. (1, 1.5)
D. (0.5, 3)
25. What is the sequence of transformations which will bring ΔQRS to ΔQ’R’S’?
A. 90 rotation clockwise about the origin
and a translation left 3
B. Reflection over the y-axis
and a translation (x, y – 6)
C. Reflection over the x-axis and a rotation of
90 about the origin
D. Dilation with a scale factor of 2
and a rotation 90 about the origin
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Refer to the graph of
YZW below.
26.Graph ∆YZW after a translation 2 units right.
and 1 unit down
28.Graph and label the image of
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27. Graph and label the image of YZW
after a reflection over the y-axis.
YZW after a dilation by a scale factor of .
Answer Key
1. ((3, –3)
2. (3, –1)
3. (–1, 4)
4. (1, 1)
5. (9, 9)
6. 30
7.
(–6, 12)
8. (–5, –1), S(–1, –1), and
9. (3, 4) 10. (–6, –5)
(–1, –6)
11.
12. 35
13. N(–2, –1), L(2, –3), M(4, 0)
14. 2, enlargement
15. (1, –3),
(4, –1),
(–5, –2)
16. They are the same shape and size.
17. (x – 4, y + 2)
18. (–2, –5)
19.
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20.
21.
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