Name:
Unit C: Unit Review Problems
Date:
Class:
1. What is the scale factor from Figure B to Figure A? _______________
What is the scale factor from Figure A to Figure B? _________________
2. What is the perimeter of figure A? ________________
What is the perimeter of figure B? ________________
How does the scale factor relate to the perimeters of figures A & B?
___________________________________________________________________________
3. Figure L not shown has a perimeter of 20. Figure L is translated 3 units left and then dilated centered at the
origin with a scale factor of ½. Figure L’ is the resulting image. What is the perimeter of Figure L’?
_________________________________________
4. What scale factor can be applied to Figure C to create Figure D?__________________
What scale factor can be applied to Figure D to create Figure C? __________________
5. Explain how to determine if two polygons are similar using the lengths of their sides.
______________________________________________________________________________
______________________________________________________________________________
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6. Determine which of the following pairs of polygons are similar. Show all of your work.
A.
B.
C.
D.
7. Determine which of the following triangles are similar to ΔDEF. (Select ALL that apply)
A.
B.
C.
D.
8. Rectangle M (not pictured) undergoes a composite transformation. The resulting image is Rectangle T.
Rectangle T is similar but not congruent to Rectangle M. Describe a two-step transformation that could have
occurred to transform Rectangle M to Rectangle T.
____________________________________________________________________________
_______________________________________________________________________
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9. Quadrilaterals JKLM and WXYZ are shown in the coordinate plane below. Quadrilateral WXYZ is the image of
quadrilateral JKLM under a transformation. Describe how the pre-image was transformed to become the
image. Be specific
______________________________________________________________________________
______________________________________________________________________________
10. The circle shown in the coordinate plane is the pre-image under a dilation centered at the origin with scale
factor 5.
List the coordinates of 4 points on the pre-image:
____________
_______________
_______________
_____________
List the coordinates of 4 points on the image (after the dilation by scale factor of 5)
_____________
____________
_______________
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______________
11. Parallelogram EFGH is shown in the coordinate plane below. Rotate EFGH 90 degrees clockwise about the
origin and then translate it 3 units down. Label the resultant image E’F’G’H’.
List the coordinates of
F’ ______________
and H’ ________________
Which statements about parallelogram E’F’G’H’ are true? Select ALL that apply.
A.
̅̅̅̅̅
𝐹′𝐺′ is parallel to
̅̅̅̅̅̅
𝐸′𝐻′
B.
̅̅̅̅̅
𝐹′𝐸′ is parallel to
̅̅̅̅̅̅
𝐺′𝐻′
C.
̅̅̅̅̅̅ is parallel to
𝐸′𝐻′
̅̅̅̅̅
𝐺′𝐹′
D.
̅̅̅̅̅ is parallel to
𝐹′𝐸′
̅̅̅̅̅̅
𝐸′𝐻′
12. Triangle QHJ is dilated with center of dilation at the origin and a scale factor of 3 and then translated right 4
units. What are the coordinates of point Q after this transformation?
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13. Two quadrilaterals are shown in the coordinate plane below. Quadrilateral ABCD was dilated with a scale
factor of 2 with the center at the origin and then rotated 180o about the origin to get the quadrilateral in
Quadrant IV.
Part A. Label the image quadrilateral in Quadrant IV using W, X, Y, and Z given that WXYZ is the image of ABCD. (be
careful with your letter placement)
Part B. Which of the following is true about rectangles ABCD and WXYZ? Check ALL that apply.
_____ 𝐴𝐵𝐶𝐷 ≅ 𝑊𝑋𝑌𝑍
_______ 𝐴𝐵𝐶𝐷 ~𝑊𝑋𝑌𝑍
_____ ∠𝐴 ≅ ∠𝑊
_______ ̅̅̅̅̅
𝐶𝐷 ~ ̅̅̅̅
𝑌𝑍
______ ABCD and WXYZ are congruent and similar
_____ ̅̅̅̅̅
𝐵𝐶 ≅ ̅̅̅̅̅
𝑋𝑌
______ ABCD and WXYZ are similar but not congruent
______ ABCD and WXYZ are congruent but not similar
14. Use the coordinate grid below to complete the following questions.
a. Rotate ∆ABC 90o clockwise and give the coordinates of the new image.
A’ _____________
B’ ______________
C’ _____________
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15. Translate triangle UHF right 4 units and up 2 units, then reflect it over the x-axis. Label the new image ABC.
Write the coordinates of the new image ABC. A ________
B _______
C ________
16. Reflect Triangle DEF over the x-axis, then reflect the image over the y-axis. Label the new image D’E’F’.
Kyle says that there’s another transformation that would have resulted in DEF transforming to D’E’F’, and that
the transformation that he’s thinking of does not include any reflections. Javon says Kyle is wrong, the only way
to cause D’E’F’ to be upside down and pointing left instead of right is by performing reflections.
Who is correct and WHY? ________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
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17. Use the picture below to complete the following:
a. Plot the line segment C (- 7, 5) D (-2, 1)
̅̅̅̅ is reflected over the x-axis? _____________
b. What are the coordinates of the image of D when line segment 𝐶𝐷
c. What are the coordinates of the image of C when line segment ̅̅̅̅
𝐶𝐷 is reflected over the line 𝑥 = 1 ___________
d. What are the coordinates of the image of D when line segment ̅̅̅̅
𝐶𝐷 is reflected over the line 𝑦 = −2 ____________
18. A transformation maps a pre-image triangle to the image triangle shown in the coordinate plane below.
If the pre-image triangle is reflected over the y-axis to get the image triangle, what are the coordinates of the
vertices of the pre-image triangle?
______________
_______________ _______________
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19. Find the missing angles in each of the triangles below, and then determine which pairs of triangles are
similar. Show all of your work.
20. Apply the given scale factors to the figures below. Draw the images. List the coordinates of the image points.
Scale factor = 1/2
Scale factor = 3/2
A’ _________ B’ _________ C’ ________ D’________
A’ _______ B’ __________ C’________ D’ _______
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