1. **State the problem:** We have two parallelograms, a smaller one with vertices Q(1,1), R(3,1), S(4,3), T(2,3) and a larger one with vertices Q'(4,3), R'(9,3), S'(12,9), T'(6,9). We want to estimate the relationship between their edge lengths and find the scale factor of the dilation. 2. **Formula and rules:** The scale factor $k$ in a dilation relates corresponding side lengths by $\text{length of image} = k \times \text{length of original}$. 3. **Calculate side lengths of the smaller figure:** - Bottom edge $QR$: distance between Q(1,1) and R(3,1) is $\sqrt{(3-1)^2 + (1-1)^2} = \sqrt{2^2 + 0} = 2$ - Left edge $QT$: distance between Q(1,1) and T(2,3) is $\sqrt{(2-1)^2 + (3-1)^2} = \sqrt{1 + 4} = \sqrt{5} \approx 2.236$ 4. **Calculate side lengths of the larger figure:** - Bottom edge $Q'R'$: distance between Q'(4,3) and R'(9,3) is $\sqrt{(9-4)^2 + (3-3)^2} = \sqrt{5^2 + 0} = 5$ - Left edge $Q'T'$: distance between Q'(4,3) and T'(6,9) is $\sqrt{(6-4)^2 + (9-3)^2} = \sqrt{2^2 + 6^2} = \sqrt{4 + 36} = \sqrt{40} \approx 6.325$ 5. **Find scale factors for corresponding edges:** - Bottom edge scale factor: $k = \frac{5}{2} = 2.5$ - Left edge scale factor: $k = \frac{6.325}{2.236} \approx 2.83$ 6. **Estimate average scale factor:** $$k \approx \frac{2.5 + 2.83}{2} = 2.665$$ 7. **Interpretation:** The larger figure's edges are about 2.7 times the smaller figure's edges, so the smaller figure's edges are less than half those of the larger figure. 8. **Answer:** The best statement is **C. The edge lengths of the smaller figure are less than half those of the larger figure**. **Final scale factor:** Approximately $2.7$ from smaller to larger figure, or equivalently about $\frac{1}{2.7} \approx 0.37$ from larger to smaller figure.