Question

the figure on the right is a scaled copy of the figure on the left, though it might have also been rotated.
answer attempt 1 out of 2
which side in the figure on the right corresponds to segment rq?
what is the scale factor?

Explanation:

First Sub - Question: Corresponding Side to \(RQ\)

To find the corresponding side to \(RQ\), we analyze the shapes. The left figure has \(RQ\) as a vertical (or near - vertical) side with a right angle at \(Q\) (since \(SQ\) is horizontal and \(RQ\) is vertical). In the right figure, side \(CA\) is vertical (or near - vertical) with a right angle at \(A\) (since \(AB\) is horizontal and \(CA\) is vertical). By comparing the orientation and the right - angled nature of the sides (considering the scaled and rotated copy), we can see that \(RQ\) corresponds to \(CA\).

Step 1: Determine the length of \(RQ\)

Looking at the grid, let's assume each grid square has a side length of 1 unit. For segment \(RQ\), we count the number of grid units it spans. From the coordinates (or by counting the vertical squares), if we assume \(R\) and \(Q\) are separated by, say, 3 grid units (we can calculate this by looking at the vertical distance between \(R\) and \(Q\) in the left figure).

Step 2: Determine the length of \(CA\)

For segment \(CA\) in the right figure, by counting the grid units, it spans 1 grid unit (vertical distance between \(C\) and \(A\)).

Step 3: Calculate the scale factor

The scale factor \(k\) is the ratio of the length of a side in the scaled (right) figure to the length of the corresponding side in the original (left) figure. So \(k=\frac{\text{Length of }CA}{\text{Length of }RQ}\). If \(RQ = 3\) and \(CA=1\), the scale factor is \(\frac{1}{3}\)? Wait, no, wait. Wait, maybe I got the original and scaled reversed. Wait, the right figure is the scaled copy of the left. So scale factor is \(\frac{\text{Length of side in scaled (right)}}{\text{Length of side in original (left)}}\). Let's re - examine. Let's take a horizontal side. In the left figure, \(SQ\): let's count the grid units. Suppose \(SQ\) is 6 units (horizontal). In the right figure, \(AB\) is 2 units (horizontal). Then the scale factor \(k=\frac{AB}{SQ}=\frac{2}{6}=\frac{1}{3}\). Let's check with \(RQ\) and \(CA\). If \(RQ\) is 3 units (vertical) and \(CA\) is 1 unit (vertical), then \(k = \frac{CA}{RQ}=\frac{1}{3}\). So the scale factor is \(\frac{1}{3}\).

Answer:

The side in the figure on the right that corresponds to segment \(RQ\) is \(CA\).

Second Sub - Question: Scale Factor