1. **Problem Statement:** Find the new coordinates of the dilated image for triangle $\triangle KLM$ with vertices $K(-2,1)$, $L(-3,-4)$, and $M(-4,1)$ under dilation with scale factor $k=2$. 2. **Formula for Dilation:** The dilation of a point $(x,y)$ with scale factor $k$ centered at the origin is given by: $$ (x', y') = (kx, ky) $$ 3. **Apply the formula to each vertex:** - For $K(-2,1)$: $$ K' = (2 \times -2, 2 \times 1) = (-4, 2) $$ - For $L(-3,-4)$: $$ L' = (2 \times -3, 2 \times -4) = (-6, -8) $$ - For $M(-4,1)$: $$ M' = (2 \times -4, 2 \times 1) = (-8, 2) $$ 4. **Final Answer:** The new coordinates after dilation are: - $K'(-4, 2)$ - $L'(-6, -8)$ - $M'(-8, 2)$