Question

Determining if a Figure Was Dilated
In rectangle ABCD, AB = 10 cm and BC = 14 cm. If rectangle EFGH is the image after a dilation, which could be its side lengths?
EF = 6 cm and FG = 10 cm
EF = 7 cm and FG = 3 cm
EF = 15 cm and FG = 20 cm
EF = 25 cm and FG = 35 cm

Answer 1

Under a dilation all lengths scale by the same factor k, so the two side lengths must be proportional to 10 and 14 (ratio 10:14 = 5:7).

Check each pair:
- 6 and 10: 6:10 = 3:5 ≠ 5:7
- 7 and 3: 7:3 ≠ 5:7
- 15 and 20: 15:20 = 3:4 ≠ 5:7
- 25 and 35: 25:35 = 5:7 — this works (k = 25/10 = 2.5, and 14·2.5 = 35).

So EF = 25 cm and FG = 35 cm.