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 op? what is the scale factor?

Explanation:

Step1: Identify corresponding sides

Since the figures are scaled - copies, we match the sides based on their relative positions. Segment $OP$ corresponds to segment $YZ$.

Step2: Assume lengths of corresponding sides

Let the length of $OP = a$ and the length of $YZ=b$. The scale factor $k$ is given by the ratio of the lengths of corresponding sides of the scaled - copy. If the figure on the right is a scaled - down copy of the figure on the left, $k=\frac{b}{a}$; if it's a scaled - up copy, $k = \frac{a}{b}$. But without knowing the actual lengths of the sides, we can't calculate a numerical value. However, if we assume the figure on the right is the smaller one, and we let the length of $OP$ be the original length and $YZ$ be the new length, the scale factor $k$ is the ratio of the length of $YZ$ to the length of $OP$.

Answer:

We need the lengths of $OP$ and $YZ$ to calculate the scale factor. If we only consider the correspondence, the side corresponding to $OP$ is $YZ$.