1. **State the problem:** We are given two triangles, UVW and U'V'W', where U'V'W' is a dilation of UVW. We need to find the scale factor of the dilation. 2. **Recall the formula for scale factor:** The scale factor $k$ of a dilation is the ratio of the length of a side in the image triangle to the corresponding side in the original triangle. 3. **Identify corresponding points:** Given points are: - $U(-5,0)$ and $U'(-1,0)$ - $V(0,-10)$ and $V'(0,-2)$ - $W(5,-10)$ and $W'(1,-2)$ 4. **Calculate lengths of corresponding sides:** - Length $UV = \sqrt{(0 - (-5))^2 + (-10 - 0)^2} = \sqrt{5^2 + (-10)^2} = \sqrt{25 + 100} = \sqrt{125} = 5\sqrt{5}$ - Length $U'V' = \sqrt{(0 - (-1))^2 + (-2 - 0)^2} = \sqrt{1^2 + (-2)^2} = \sqrt{1 + 4} = \sqrt{5}$ 5. **Calculate scale factor:** $$k = \frac{U'V'}{UV} = \frac{\sqrt{5}}{5\sqrt{5}}$$ 6. **Simplify the fraction:** $$k = \frac{\sqrt{5}}{5\sqrt{5}} = \frac{\cancel{\sqrt{5}}}{5\cancel{\sqrt{5}}} = \frac{1}{5}$$ 7. **Conclusion:** The scale factor of the dilation is $\boxed{\frac{1}{5}}$.