rectangle abcd was dilated to create rectangle abcd using point r as the center of dilation. if rd = 15…

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

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

Answer

Explanation:

Step1: Find the scale - factor

The ratio of corresponding side lengths gives the scale - factor. For example, comparing side (A'B') and (AB), the length of (A'B' = 3) and (AB = 9). The scale - factor (k=\frac{A'B'}{AB}=\frac{3}{9}=\frac{1}{3}).

Step2: Calculate (RD')

We know that if a point (D) is dilated from center (R) to (D') with scale - factor (k), then (RD'=k\times RD). Given (RD = 15) and (k=\frac{1}{3}), so (RD'=\frac{1}{3}\times15 = 5).

Answer:

5 units