Math 30-3
Unit 5 – Transformations
Year End Review Guide
T.1 - Demonstrate an understanding of transformations on
a 2-D shape or a 3-D object, including:
• translations
• rotations
• reflections
• dilations.
[C, CN, R, T, V]
[ICT: C6–3.4]
Dilations
1. Katya creates handmade sets of nesting dolls, which she sells to craft and souvenir stores. One
set includes five dolls. The mid-sized doll has a middle diameter of 7 cm and a height of 12 cm.
a. The largest doll has a diameter of 12 cm. If it is a dilation of the mid-sized doll, what
scale factor was used? What is the height of the largest doll?
b. The smallest doll is a dilation of the mid-sized doll, by a scale factor of 0.3. What are the
diameter and height of the smallest doll?
c. Katya made another set of dolls. In the new set, the largest doll has a diameter of 8.75
cm and a height of 15.6 cm. Is this a dilation of the first set of dolls? Explain.
Math 30-3
Translations
2. A point A(-5, 3) is translated 3 units right and 4 units down. What are its new
coordinates?
3. Translate the following shape 5 units left and 3 down.
LABEL THE NEW COORDINATES!!!
4. Describe the translation(s) that have taken place to move object A to object B?
Math 30-3
Reflections
5. A point C(-5, 3) is reflected across the y-axis. What are its new coordinates?
6. Reflect the following shape across the indicated line.
LABEL THE VERTICES (A’, B’, C’, D’, E’)
7. Draw in the line of reflection, for the reflection of object A to object B.
Math 30-3
Rotations
8. Rotate the following diagram 90° clockwise about the origin.
LABEL THE NEW VERTICES!!! (A’, B’, C’, D’)
9. Rotate the following diagram 270° counter-clockwise about the point P.
LABEL THE NEW VERTICES!!! (A’, B’, C’, D’)
Math 30-3
Combining Transformations
10. a) Rotate the following shape 270° clockwise about the origin.
b) translate the image 5 units right and 3 units up.
c) reflect the image over the x-axis.
SHOW ALL INTERMEDIATE STEPS!
LABEL THE NEW VERTICES!!! (A’, B’, C’)
Math 30-3
11. a) Reflect the following shape across the y-axis.
b) Rotate the image 270° clockwise about the origin.
c) Translate the image 4 units right and 2 units up.
SHOW ALL INTERMEDIATE STEPS!
LABEL THE NEW VERTICES!!! (A’, B’, C’, D’, E’)
Math 30-3
12. Shape A underwent a combination of transformations to become shape B. What
transformations could have been applied to create the image?
A
B