Question

polygon r is a scaled copy of polygon q. what scale factor takes polygon q to polygon r?

Explanation:

Step1: Recall scale - factor formula

The scale factor $k$ from polygon $Q$ to polygon $R$ is given by the ratio of corresponding side - lengths. Let's take one pair of corresponding sides.

Step2: Calculate the scale factor

If we take the side of length $0.3$ in polygon $Q$ and the corresponding side of length $0.15$ in polygon $R$, then $k=\frac{\text{side - length in }R}{\text{side - length in }Q}$. So, $k = \frac{0.15}{0.3}$.
\[k=\frac{0.15}{0.3}=\frac{15}{30}=\frac{1}{2}=0.5\]
We can also check with another pair of corresponding sides. Taking the side of length $0.32$ in polygon $Q$ and the corresponding side of length $0.16$ in polygon $R$, we have $k=\frac{0.16}{0.32}=\frac{16}{32}=\frac{1}{2}=0.5$.

Answer:

$0.5$