Question

△abc is dilated by a factor of 1/3 to produce △abc. what is ac, the length of ac after the dilation? what is the measure of ∠a?

Explanation:

Step1: Recall Dilation Properties

Dilation scales lengths by the scale factor and preserves angle measures. For length \( A'C' \), original \( AC = 15 \), scale factor \( k=\frac{1}{3} \).
\( A'C' = k \times AC \)

Step2: Calculate \( A'C' \)

Substitute \( k = \frac{1}{3} \) and \( AC = 15 \):
\( A'C'=\frac{1}{3} \times 15 = 5 \)

Step3: Determine \( \angle A' \)

Dilation preserves angles, so \( \angle A' = \angle A = 37^\circ \).

Answer:

Length of \( \overline{A'C'} \) is \( 5 \), measure of \( \angle A' \) is \( 37^\circ \).