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 qs?
what is the scale factor?

(options: xw, wv, vy, yx)

Explanation:

Part 1: Corresponding Side to \( QS \)

To find the corresponding side, we analyze the shapes. The left figure ( \( QRST \) - like) and right figure ( \( XWVY \) - like) are scaled copies. Segment \( QS \) connects \( Q \) and \( S \). By matching the angle and side relationships (considering rotation and scaling), the side \( VY \) in the right figure corresponds to \( QS \) (since the vertices' order and angle properties match when aligning the scaled copy).

Step 1: Determine Lengths (Assume Grid Units)

Suppose the length of \( QS \) in the left figure is, say, \( 4 \) units (from grid analysis), and the length of \( VY \) (corresponding side) in the right figure is \( 2 \) units.

Step 2: Calculate Scale Factor

Scale factor \( = \frac{\text{Length of side in scaled copy (right)}}{\text{Length of corresponding side in original (left)}} \). So, \( \frac{2}{4} = \frac{1}{2} \). (Actual calculation depends on grid measurements, but the key is comparing corresponding sides' lengths.)

Answer:

\( VY \)

Part 2: Scale Factor