Question

polygon r is a scaled copy of polygon q.
image of polygon q with side lengths 0.3, 0.3, 0.32
image of polygon r with side lengths 0.15, 0.15, 0.16
what scale factor takes polygon q to polygon r?

Explanation:

Step1: Recall scale factor formula

The scale factor from a figure to its scaled copy is the ratio of a corresponding side length of the copy to the original figure. So, scale factor \(=\frac{\text{Length of side in } R}{\text{Length of corresponding side in } Q}\).

Step2: Choose a corresponding side

Let's take the top side: in \(Q\) it's \(0.3\), in \(R\) it's \(0.15\).

Step3: Calculate the ratio

Scale factor \(=\frac{0.15}{0.3}\) \( = 0.5\). We can check with another side, like the vertical side: \(\frac{0.15}{0.3}=0.5\), or the bottom side: \(\frac{0.16}{0.32}=0.5\). All give the same ratio.

Answer:

\(0.5\)