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 5 units 6 units 9 units

Explanation:

Step1: Find the scale factor

The scale factor \(k\) of dilation is the ratio of corresponding side lengths. For example, \(\frac{A'B'}{AB}\). Given \(A'B' = 3\) and \(AB=9\), then \(k=\frac{A'B'}{AB}=\frac{3}{9}=\frac{1}{3}\).

Step2: Use the scale factor to find \(RD'\)

We know that if a figure is dilated with center \(R\), then the ratio of the distances from the center of dilation is equal to the scale factor. That is \(\frac{RD'}{RD}=k\). Given \(RD = 15\) and \(k=\frac{1}{3}\), then \(RD'=RD\times k\).
Substitute the values: \(RD'=15\times\frac{1}{3}\).
Calculate \(15\times\frac{1}{3}=5\).

Answer:

5 units