1. **State the problem:** We have two trapezoids, RSTU and R'S'T'U', where R'S'T'U' is a dilation of RSTU. We need to find the scale factor of the dilation. 2. **Recall the formula for scale factor:** The scale factor $k$ in a dilation is the ratio of any corresponding side length or coordinate difference in the image to the pre-image. 3. **Choose corresponding points:** Let's use points R and R' to find the scale factor. Coordinates are $R(-6,6)$ and $R'(-2,2)$. 4. **Calculate the scale factor using the x-coordinates:** $$k = \frac{x_{R'}}{x_R} = \frac{-2}{-6} = \frac{1}{3}$$ 5. **Calculate the scale factor using the y-coordinates:** $$k = \frac{y_{R'}}{y_R} = \frac{2}{6} = \frac{1}{3}$$ 6. **Verify with another pair of points:** Using S and S', $S(8,6)$ and $S'(3,2)$: $$k_x = \frac{3}{8}, \quad k_y = \frac{2}{6} = \frac{1}{3}$$ Since $k_x$ is not equal to $k_y$ here, check T and T': $T(6,-6)$ and $T'(2,-2)$: $$k_x = \frac{2}{6} = \frac{1}{3}, \quad k_y = \frac{-2}{-6} = \frac{1}{3}$$ 7. **Conclusion:** The consistent scale factor is $\frac{1}{3}$. **Final answer:** The scale factor of the dilation is $\boxed{\frac{1}{3}}$.