Question

if line segment uv is dilated by a scale factor greater than 1, which could be the image line segment?
a uv 6 mm
b uv 9 mm
c uv 18 mm
d uv 24 mm

Explanation:

Step1: Recall dilation with scale factor >1

Dilation with a scale factor greater than 1 enlarges the original figure. The length of the image segment should be greater than the original length (18 mm).

Step2: Analyze each option

• Option A: 6 mm < 18 mm (reduction, scale factor <1)
• Option B: 9 mm < 18 mm (reduction, scale factor <1)
• Option C: 18 mm = 18 mm (scale factor =1, not greater than 1)
• Option D: 24 mm > 18 mm (enlargement, scale factor >1)

Answer:

D. \( U'V' \) with length 24 mm