1. **State the problem:** We have two trapezoids, KLMN and K'L'M'N', where K'L'M'N' is a dilation of KLMN. We need to find the scale factor of the dilation. 2. **Recall the scale factor definition:** The scale factor of a dilation is the ratio of any corresponding lengths in the image to the preimage. 3. **Identify corresponding points:** K corresponds to K', L to L', M to M', and N to N'. 4. **Calculate lengths of corresponding sides:** - Length KL = distance between K(-8,10) and L(6,10) = $|6 - (-8)| = 14$ - Length K'L' = distance between K'(-4,8) and L'(4,8) = $|4 - (-4)| = 8$ 5. **Calculate scale factor:** $$\text{scale factor} = \frac{\text{length of image side}}{\text{length of preimage side}} = \frac{8}{14}$$ 6. **Simplify the fraction:** $$\frac{8}{14} = \frac{4}{7}$$ 7. **Verify with another pair:** - Length MN = distance between M(6,0) and N(-8,-10) = $\sqrt{(6 - (-8))^2 + (0 - (-10))^2} = \sqrt{14^2 + 10^2} = \sqrt{196 + 100} = \sqrt{296}$ - Length M'N' = distance between M'(4,2) and N'(-4,-6) = $\sqrt{(4 - (-4))^2 + (2 - (-6))^2} = \sqrt{8^2 + 8^2} = \sqrt{64 + 64} = \sqrt{128}$ Calculate ratio: $$\frac{\sqrt{128}}{\sqrt{296}} = \sqrt{\frac{128}{296}} = \sqrt{\frac{32}{74}} = \sqrt{\frac{16}{37}}$$ This is approximately $\sqrt{0.4324} \approx 0.657$, which is close to $\frac{4}{7} \approx 0.571$, so the scale factor from the horizontal sides is the best exact ratio. **Final answer:** The scale factor of the dilation is $\boxed{\frac{4}{7}}$.