1. **State the problem:** Determine if the transformation from triangle $\triangle GHJ$ to $\triangle G'H'J'$ is a dilation and find the scale factor. 2. **Given points:** - $H(-8,8)$, $G(6.5,5.5)$, $J(7.5,-7.5)$ - $H'(-4,4)$, $G'(3.25,2.75)$, $J'(3.75,-3.75)$ 3. **Formula for scale factor in dilation:** $$k = \frac{\text{image coordinate}}{\text{pre-image coordinate}}$$ 4. **Calculate scale factors for each vertex:** - For $H$ to $H'$: $$k_H = \frac{-4}{-8} = \frac{1}{2}, \quad k_H = \frac{4}{8} = \frac{1}{2}$$ - For $G$ to $G'$: $$k_G = \frac{3.25}{6.5} = \frac{1}{2}, \quad k_G = \frac{2.75}{5.5} = \frac{1}{2}$$ - For $J$ to $J'$: $$k_J = \frac{3.75}{7.5} = \frac{1}{2}, \quad k_J = \frac{-3.75}{-7.5} = \frac{1}{2}$$ 5. **Interpretation:** All scale factors are consistent and equal to $\frac{1}{2}$. 6. **Conclusion:** The transformation is a dilation with scale factor $k=\frac{1}{2}$, confirming the smaller triangle is a scaled version of the original. **Final answer:** The transformation from $\triangle GHJ$ to $\triangle G'H'J'$ is a dilation with scale factor $\boxed{\frac{1}{2}}$.