Question

the figure on the right is a scaled copy of the figure on the left.
which side in the figure on the right corresponds to segment pq?
what is the scale factor?

Explanation:

Step1: Identify Corresponding Sides

In similar figures (scaled copies), corresponding sides are in proportion and have the same relative position. Looking at the labels, segment \( PS \) (left figure) corresponds to segment \( CH \) (right figure) as they are the top horizontal sides of their respective figures.

Step2: Determine Scale Factor

To find the scale factor, we compare the lengths of corresponding sides. Let's assume the length of \( PS \) is, say, 3 units (from grid estimation) and \( CH \) is 1 unit? Wait, no, maybe better to count grid squares. Wait, looking at the vertical side: left figure's vertical side (e.g., \( PR \)): let's count the vertical grid squares. Suppose left figure's vertical side has length 3 (from top to bottom), right figure's vertical side (e.g., \( CE \)) has length 1? Wait, no, maybe the left figure's side \( PS \) (horizontal) and right figure's \( CH \) (horizontal). Let's check the number of grid units. If left figure's \( PS \) spans, say, 3 grid units, and right figure's \( CH \) spans 1 grid unit? Wait, no, maybe the scale factor is \( \frac{1}{3} \)? Wait, no, let's see the size. The right figure is smaller. Let's take corresponding vertical sides: left figure's vertical side (e.g., \( PR \)): from top to bottom, how many grids? Let's say left figure's vertical side is 3 units, right figure's vertical side (e.g., \( CE \)) is 1 unit. So scale factor is \( \frac{1}{3} \)? Wait, no, maybe the left figure's side \( PS \) and right figure's \( CH \): if \( PS \) is length 3, \( CH \) is length 1, then scale factor is \( \frac{1}{3} \). Wait, maybe I got it reversed. Wait, scale factor is (length of image)/(length of original). So original is left, image is right. So scale factor \( k = \frac{\text{length of } CH}{\text{length of } PS} \). If \( PS \) is 3, \( CH \) is 1, then \( k = \frac{1}{3} \).

Answer:

Corresponding side to \( PS \): \( CH \)
Scale factor: \( \frac{1}{3} \) (assuming the original figure is left, scaled copy is right; if original is right, scale factor would be 3, but since it's a scaled copy (right is smaller), scale factor is \( \frac{1}{3} \))