1. **State the problem:** We need to find the scale factor used to transform rectangle X into rectangle Y and express it as a percentage to one decimal place. 2. **Identify given dimensions:** - Rectangle X: height = 7.0 cm, width = 24.5 cm - Rectangle Y: height = 2.0 cm, width = 7.0 cm 3. **Formula for scale factor:** The scale factor $k$ is the ratio of a corresponding length in the image to the original length: $$k = \frac{\text{length in } Y}{\text{length in } X}$$ 4. **Calculate scale factor using height:** $$k = \frac{2.0}{7.0}$$ 5. **Simplify the fraction:** $$k = \frac{2.0}{7.0} \approx 0.2857$$ 6. **Calculate scale factor using width:** $$k = \frac{7.0}{24.5}$$ 7. **Simplify the fraction:** $$k = \frac{7.0}{24.5} \approx 0.2857$$ 8. **Confirm scale factor is consistent:** Both height and width give approximately the same scale factor $0.2857$. 9. **Convert scale factor to percentage:** $$\text{Scale factor \%} = k \times 100 = 0.2857 \times 100 = 28.57\%$$ 10. **Round to one decimal place:** $$28.57\% \approx 28.6\%$$ **Final answer:** The scale factor is **28.6 %**.