1. **State the problem:** We have triangle LMN with vertices L(1, -2), M(3, 0), and N(2, -3). We want to perform a dilation with scale factor $k=5$. 2. **Formula for dilation:** To dilate a point $(x,y)$ by scale factor $k$ about the origin, the new coordinates $(x', y')$ are given by: $$x' = kx$$ $$y' = ky$$ 3. **Apply dilation to each vertex:** - For $L(1, -2)$: $$L' = (5 \times 1, 5 \times -2) = (5, -10)$$ - For $M(3, 0)$: $$M' = (5 \times 3, 5 \times 0) = (15, 0)$$ - For $N(2, -3)$: $$N' = (5 \times 2, 5 \times -3) = (10, -15)$$ 4. **Final answer:** The vertices of the dilated triangle are: $$L'(5, -10), M'(15, 0), N'(10, -15)$$ This means the triangle has been enlarged by a factor of 5 from the origin, keeping the shape but increasing the size proportionally.