1. **State the problem:** We have two rectangles, KLMN and K'L'M'N', where K'L'M'N' is a dilation of KLMN. We need to find the scale factor of this dilation. 2. **Recall the formula for scale factor:** The scale factor $k$ in a dilation is the ratio of any corresponding side length in the image to the corresponding side length in the preimage. 3. **Find side lengths of rectangle KLMN:** - Length of side KL: distance between points $K(-6,6)$ and $L(-6,0)$ is $$|6 - 0| = 6$$ - Length of side LM: distance between points $L(-6,0)$ and $M(3,0)$ is $$|3 - (-6)| = 9$$ 4. **Find side lengths of rectangle K'L'M'N':** - Length of side K'L': distance between points $K'(-2,2)$ and $L'(-2,0)$ is $$|2 - 0| = 2$$ - Length of side L'M': distance between points $L'(-2,0)$ and $M'(1,0)$ is $$|1 - (-2)| = 3$$ 5. **Calculate scale factor:** - Using vertical sides: $$k = \frac{K'L'}{KL} = \frac{2}{6} = \frac{1}{3}$$ - Using horizontal sides: $$k = \frac{L'M'}{LM} = \frac{3}{9} = \frac{1}{3}$$ 6. **Conclusion:** Both ratios agree, so the scale factor of the dilation is $$\boxed{\frac{1}{3}}$$.