in $ \triangle abc $, $ \angle abc $ is a right angle, $ ab = 3 $ units, and $ bc = 2 $ units. $ \triangle abc $ is dilated by a scale factor of 0.5 with point $ b $ as the center of dilation, resulting in the image $ \triangle abc $. which statement about $ \overline{ab} $ is true?
a. $ \overline{ab} $ is 3 units long but lies on a different line than $ \overline{ab} $.
b. $ \overline{ab} $ is 1.5 units long and lies on the same line as $ \overline{ab} $.
c. $ \overline{ab} $ is 1.5 units long but lies on a different line than $ \overline{ab} $.
d. $ \overline{ab} $ is 3 units long and lies on the same line as $ \overline{ab} $.

Question

Accepted Answer

# Explanation:
## Step1: Recall Dilation Properties
Dilation with center $ B $ means $ B $ is fixed ($ B' = B $). The scale factor is $ 0.5 $, so $ A'B' = \text{scale factor} \times AB $.
$ AB = 3 $, so $ A'B' = 0.5 \times 3 = 1.5 $ units.

## Step2: Analyze Line Collinearity
Since dilation from $ B $ (center) keeps $ A $, $ B $, and $ A' $ collinear (because dilation preserves the line through the center and the point). So $ \overline{A'B'} $ (same as $ \overline{A'B} $) lies on the same line as $ \overline{AB} $.

# Answer: B. $\overline{A'B'}$ is 1.5 units long and lies on the same line as $\overline{AB}$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Recall Dilation Properties

Step2: Analyze Line Collinearity

Answer: