Question

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

Explanation:

Step1: Recall scale - factor formula

The scale factor $k$ from polygon $P$ to polygon $Q$ is given by the ratio of corresponding side lengths. Let's take a pair of corresponding sides. For example, if we consider the side of length 8 in polygon $P$ and the corresponding side of length 4 in polygon $Q$.

Step2: Calculate the scale factor

$k=\frac{\text{Length of side in }Q}{\text{Length of corresponding side in }P}=\frac{4}{8}=\frac{1}{2}$
We can check with other side - length pairs. For the side of length 18 in polygon $P$ and the corresponding side of length 9 in polygon $Q$, $\frac{9}{18}=\frac{1}{2}$, and for the side of length 14 in polygon $P$ and the corresponding side of length 7 in polygon $Q$, $\frac{7}{14}=\frac{1}{2}$.

Answer:

$\frac{1}{2}$