The problem states that the figure on the right is a scaled copy of the figure on the left, and asks which side on the right corresponds to segment $RO$ in the left figure, as well as the scale factor between the figures.

Corresponding Segment:

To identify which side on the right corresponds to $RO$ on the left, we can match the letters of the figures. Based on the labeling in both figures:

• Segment $RO$ (right-hand side of the smaller quadrilateral) corresponds to segment $IL$ (right-hand side of the larger quadrilateral).

This is confirmed since both $RO$ and $IL$ are opposite the corresponding $QO$ and $JL$ segments in their respective shapes.

Scale Factor:

The scale factor is given as $\frac{1}{3}$, meaning the smaller shape on the left is $\frac{1}{3}$ the size of the larger shape on the right. This suggests that each side of the smaller figure is scaled by this factor to produce the corresponding side on the larger figure.

Would you like more details or have additional questions on this? Here are five related questions to expand this concept:

1. How do you determine corresponding sides in similar figures?
2. What mathematical properties do scaled copies retain (e.g., angles, proportions)?
3. Can you explain how to calculate the scale factor given the lengths of two corresponding sides?
4. How does the area change when you apply a scale factor to a geometric figure?
5. How would you find the length of a side in one figure if you know the corresponding side in the other figure and the scale factor?

Tip: When working with scale factors, remember that lengths are proportional, but areas scale by the square of the factor.