Dilation
Answers are for parents and teachers.
1
k = 3/5 and OP = 20 cm. Find OP′.
OP′ = 3/5 × 20 = 12 cm.
2
Dilate the triangle (2, 2), (6, 2), (2, 5) about the origin with k = 1.5.
(3, 3), (9, 3), (3, 7.5).
3
AB = 15, AD = 9, AC = 20, AE = 12, BC = 25. Is DE ∥ BC? Find DE.
9 ÷ 15 = 12 ÷ 20 = 3/5, so yes. DE = 3/5 × 25 = 15.
4
P′(10, −15) is the image of P under k = 5 about the origin. Find P.
P = (10 ÷ 5, −15 ÷ 5) = (2, −3).
5
A rectangle 5 cm by 4 cm is dilated with k = 3. Find the area of the image and compare with the original.
The image is 15 by 12, area 180. The original has area 20, and 180 = 9 × 20 = 3² × 20.