1. **State the problem:** We need to find the image of triangle $\triangle EFG$ after a dilation centered at the origin with scale factor $\frac{1}{5}$. The original vertices are $E(-10, 10)$, $F(0, 10)$, and $G(-4, -10)$. 2. **Formula for dilation:** The dilation of a point $(x, y)$ about the origin with scale factor $k$ is given by: $$ (x', y') = (kx, ky) $$ 3. **Apply the dilation to each vertex:** - For $E(-10, 10)$: $$ E' = \left(\frac{1}{5} \times -10, \frac{1}{5} \times 10\right) = (-2, 2) $$ - For $F(0, 10)$: $$ F' = \left(\frac{1}{5} \times 0, \frac{1}{5} \times 10\right) = (0, 2) $$ - For $G(-4, -10)$: $$ G' = \left(\frac{1}{5} \times -4, \frac{1}{5} \times -10\right) = \left(-\frac{4}{5}, -2\right) $$ 4. **Conclusion:** The image $\triangle E'F'G'$ after dilation has vertices: $$ E'(-2, 2), \quad F'(0, 2), \quad G'\left(-\frac{4}{5}, -2\right) $$ This completes the dilation process.