Question

rectangle abcd was dilated to create rectangle abcd using point r as the center of dilation. if rd = 15, what is rd? 3 units 9 units 5 units 6 units

Explanation:

Step1: Find the scale factor of dilation

The length of \( AB = 9 \) and \( A'B' = 3 \), so the scale factor \( k=\frac{A'B'}{AB}=\frac{3}{9}=\frac{1}{3} \). Alternatively, using the vertical sides: \( BC = 12 \) and \( B'C' = 4 \), so \( k=\frac{B'C'}{BC}=\frac{4}{12}=\frac{1}{3} \).

Step2: Apply the scale factor to \( RD \)

Since dilation with center \( R \) scales distances from \( R \) by the scale factor \( k \), we have \( RD'=k\times RD \). Given \( RD = 15 \) and \( k=\frac{1}{3} \), then \( RD'=\frac{1}{3}\times15 = 5 \).

Answer:

5 units