1. **State the problem:** We are given two rectangles, KLMN and its dilation K'L'M'N'. We need to find the scale factor of the dilation. 2. **Understand dilation:** A dilation with center at the origin (0,0) changes the dimensions of a figure by a scale factor \(k\). Each point \((x,y)\) maps to \((kx, ky)\). 3. **Identify coordinates:** - Original rectangle KLMN has points: - \(K(-6,6)\) - \(L(-6,2)\) - \(M(3,2)\) - \(N(3,6)\) - Dilated rectangle K'L'M'N' has points: - \(K'(-2,2)\) - \(L'(-2,1)\) - \(M'(1,1)\) - \(N'(1,2)\) 4. **Calculate scale factor:** Use point \(K\) and its image \(K'\) for calculation: - Original point \(K=(-6,6)\) - Image point \(K'=(-2,2)\) Since dilation center is at the origin, the scale factor \(k\) satisfies: $$k = \frac{x_{K'}}{x_K} = \frac{-2}{-6} = \frac{1}{3}$$ Check y-coordinates as well: $$k = \frac{y_{K'}}{y_K} = \frac{2}{6} = \frac{1}{3}$$ 5. **Conclusion:** The scale factor of the dilation is \(\frac{1}{3}\). **Final answer:** \(\boxed{\frac{1}{3}}\)