Question

rectangle abcd was dilated to create rectangle abcd.
what is ab?
○ 6 units
○ 7.6 units
○ 9.5 units
○ 12 units
(diagram shows rectangle abcd with ab = 15, bc = 9.5; rectangle abcd with bc = 3.8)

Explanation:

Step1: Find the scale factor

The vertical sides of the rectangles are \( 3.8 \) (for ABCD) and \( 9.5 \) (for A'B'C'D). The scale factor \( k \) is \( \frac{9.5}{3.8} = 2.5 \).

Step2: Use scale factor to find AB

The length of \( A'B' \) is \( 15 \). Since dilation preserves the ratio, \( AB=\frac{A'B'}{k}=\frac{15}{2.5} = 6 \).

Answer:

6 units