1. Unit 2 – Similarity, Congruence, and Proofs
Review Quiz #1
Investigating Properties of Dilations

2. Does the graph below represent a dilation? Why or why not?
Question 1
Does the graph below represent a dilation? Why or why not?
NO, because the scale factors of the image sides are not all consistent with the preimage sides.

3. Determine the scale factor of the dilation below.
Question 2
Determine the scale factor of the dilation below.
𝑘= 1 2

4. Determine the scale factor of the dilation below.
Question 3
Determine the scale factor of the dilation below.
𝑘=2.5

5. Question 4
𝐴𝐵 is 6.7 units long. If 𝐴𝐵 is dilated by a scale factor of 𝑘=3.2, what is the length of 𝐴′𝐵′ ?
21.44 𝑢𝑛𝑖𝑡𝑠

6. Question 5
∆𝐹𝐺𝐻 has vertices 𝐹 3,−5 , 𝐺 8,−6 and 𝐻(6,−7). If ∆𝐹𝐺𝐻 is dilated through the origin with a scale factor of 3 4 , what are the vertices of ∆𝐹′𝐺′𝐻′?
𝐹′ 2.25,−3.75 , 𝐺′ 6,−4.5 and 𝐻′(4.5,−5.25)

7. Question 6
Compare ∆𝑇𝑈𝑉 to ∆𝑇′𝑈′𝑉′. Does the diagram below show a dilation? Why or why not?
YES, the diagram represents a dilation because the scale factors are consistent

8. Question 7
Compare ∆𝑄𝑅𝐶 to ∆𝑄 𝑅 ′ 𝐶. Does the diagram below show a dilation? Why or why not?
No, the diagram does not represent a dilation because the scale factors are inconsistent

9. Question 8
Compare parallelogram 𝐶𝑀𝑁𝑂 to parallelogram 𝐶 𝑀 ′ 𝑁 ′ 𝑂. Does the diagram below show a dilation? Why or why not?
No, the diagram does not represent a dilation because the scale factors are inconsistent

10. 𝑘=2 What is the scale factor of the dilation pictured below?
Question 9
What is the scale factor of the dilation pictured below?
𝑘=2

11. 𝑘= 1 2 or 0.5 What is the scale factor of the dilation pictured below?
Question 10
What is the scale factor of the dilation pictured below?
𝑘= 1 2 or 0.5

12. Question 11
If a dilation with a scale factor of takes place, what type of dilation is this?
Enlargement

13. Question 12
If a dilation with a scale factor of .95 takes place, what type of dilation is this?
Reduction

14. 𝑘=2.5 What is the scale factor of the dilation pictured below?
Question 13
What is the scale factor of the dilation pictured below?
𝑘=2.5

15. 𝑘=1.25 What is the scale factor of the dilation pictured below?
Question 14
What is the scale factor of the dilation pictured below?
𝑘=1.25

16. Question 15
If 𝐴𝐵 has a length of 6.5 units, what is the length of 𝐴′𝐵′ under a dilation with a scale factor of 𝑘=2.5?
16.25 𝑢𝑛𝑖𝑡𝑠

17. Question 16
If 𝐶𝐷 has a length of units, what is the length of 𝐶 ′ 𝐷′ under a dilation with a scale factor of 75%?
27.9 𝑢𝑛𝑖𝑡𝑠

18. Question 17
If ∆𝑃𝑄𝑅 has vertices with the coordinates P (–6, 4), Q (5, 9), and R (–3, –6)what are the vertices of ∆ 𝑃 ′ 𝑄 ′ 𝑅′ under a dilation with a scale factor of and the center at the origin, (0, 0)?
P′(–3.75, 2.5), Q′(3.125, 5.625), and R′(–1.875, –3.75)

19. H′(–12.25, −5.25), J′(−6.75, −10.5), and K′(–10.5, –14)
Question 18
If ∆𝐻𝐽𝐾 has vertices with the coordinates H (–7, –3), J (–5, –6), and K (–6, –8) what are the vertices of ∆ 𝐻 ′ 𝐽 ′ 𝐾′ under a dilation with a scale factor of 1.75 and the center at the origin, (0, 0)?
H′(–12.25, −5.25), J′(−6.75, −10.5), and K′(–10.5, –14)

20. If ∆𝑀𝑁𝑂 has vertices with the coordinates M (–5, 8),
Question 19
If ∆𝑀𝑁𝑂 has vertices with the coordinates M (–5, 8),
N (7, –3), and O (–10, –4) what are the vertices of ∆ 𝑀 ′ 𝑁 ′ 𝑂′ under a dilation with a scale factor of 120% and the center at the origin, (0, 0)?
M′(–6, 9.6), N′(8.4, −3.6), and O′(–12, –4.8)

21. If ∆𝐴𝐵𝐷 has vertices with the coordinates A (6, 5),
Question 20
If ∆𝐴𝐵𝐷 has vertices with the coordinates A (6, 5),
B (2, 2), and D (–3, 4) what are the vertices of ∆ 𝐴 ′ 𝐵 ′ 𝐷′ under a dilation with a scale factor of 50% and the center at the origin, (0, 0)?
A′ (3, 2.5), B′(1, 1), and D′(–1.5, 2)