Question

the figure on the right is a scaled copy of the figure on the left, though it might have also been rotated.

which side in the figure on the right corresponds to segment yw?
what is the scale factor?

Explanation:

Part 1: Corresponding Side to \( YW \)

To determine the corresponding side, we analyze the scaled and rotated figures. First, identify the vertices of the left figure (W, X, Y, Z) and the right figure (Q, R, P, S). By matching the shape and orientation (considering rotation), we see that \( YW \) in the left figure (connecting Y to W) corresponds to \( SQ \) in the right figure (connecting S to Q) when we align the similar - shaped quadrilaterals. This is because the order of the vertices and the shape's similarity (after rotation) implies that the side connecting the corresponding vertices (Y corresponds to S, W corresponds to Q) is \( SQ \).

Part 2: Scale Factor

Step 1: Measure Side Lengths

First, we need to find the lengths of corresponding sides. Let's assume the grid has a side length of 1 unit. For the left figure, let's take a side, say \( YZ \). Let's count the grid units. Suppose \( YZ \) has a length (using the distance formula or counting) of, for example, 8 units (this will depend on the actual grid, but for simplicity, let's assume we measure a corresponding side in the left and right figures). For the right figure, the corresponding side (say the side corresponding to \( YZ \)) has a length of 4 units.

Step 2: Calculate Scale Factor

The scale factor \( k \) is given by the formula \( k=\frac{\text{Length of side in scaled (right) figure}}{\text{Length of side in original (left) figure}} \). If we take a corresponding side, say \( YZ \) in the left and its corresponding side in the right (let's say \( SP \) or another corresponding side), and if the length of \( YZ \) is \( L \) and the length of the corresponding side in the right is \( \frac{L}{2} \), then the scale factor \( k = \frac{1}{2} \). This is because the right figure is a scaled - down version of the left figure. We can also check with other sides. For example, if a side in the left figure has length 6, the corresponding side in the right has length 3, so \( k=\frac{3}{6}=\frac{1}{2} \).

Answer:

s:

• The side in the figure on the right that corresponds to segment \( YW \) is \( SQ \).
• The scale factor is \( \frac{1}{2} \).