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

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.

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

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

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

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)

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

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

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

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

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

Question 11 If a dilation with a scale factor of 4 3 takes place, what type of dilation is this? Enlargement

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

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

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

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

Question 16 If 𝐶𝐷 has a length of 37.2 units, what is the length of 𝐶 ′ 𝐷′ under a dilation with a scale factor of 75%? 27.9 𝑢𝑛𝑖𝑡𝑠

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 5 8 and the center at the origin, (0, 0)? P′(–3.75, 2.5), Q′(3.125, 5.625), and R′(–1.875, –3.75)

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)

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)

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)