1. **State the problem:** We have two similar quadrilaterals RSTU and VWXY. We know some side lengths of RSTU and one side length of VWXY, and we need to find the length of side XY. 2. **Recall the property of similar figures:** Corresponding sides of similar figures are proportional. This means the ratio of any two corresponding sides in one figure equals the ratio of the corresponding sides in the other figure. 3. **Identify corresponding sides:** Given sides in RSTU are 16 and 8. The side in VWXY corresponding to 16 is 17.5. We want to find the side XY corresponding to 8. 4. **Set up the proportion:** $$\frac{16}{17.5} = \frac{8}{XY}$$ 5. **Solve for XY:** Cross multiply: $$16 \times XY = 8 \times 17.5$$ 6. **Simplify:** $$16XY = 140$$ 7. **Divide both sides by 16:** $$XY = \frac{140}{16}$$ 8. **Show cancellation:** $$XY = \frac{\cancel{140}}{\cancel{16}} = \frac{35}{4} = 8.75$$ 9. **Final answer:** The length of side XY is $8.75$ units.