1. **Problem Statement:** We have a triangle with vertices K(-1,-2), L(-1,2), and M(2,-2). We need to find the coordinates of the vertices after a dilation centered at the origin with a scale factor of 3. 2. **Formula for Dilation:** If a point $(x,y)$ is dilated by a scale factor $k$ centered at the origin, the new coordinates $(x',y')$ are given by: $$ (x', y') = (kx, ky) $$ 3. **Apply the formula to each vertex:** - For $K(-1,-2)$: $$ K' = (3 \times -1, 3 \times -2) = (-3, -6) $$ - For $L(-1,2)$: $$ L' = (3 \times -1, 3 \times 2) = (-3, 6) $$ - For $M(2,-2)$: $$ M' = (3 \times 2, 3 \times -2) = (6, -6) $$ 4. **Explanation:** Dilation centered at the origin multiplies each coordinate by the scale factor. Since the scale factor is 3, each $x$ and $y$ coordinate is tripled, moving the points farther from the origin but keeping the shape similar. 5. **Final Answer:** - $K' = (-3, -6)$ - $L' = (-3, 6)$ - $M' = (6, -6)$