1. **State the problem:** We are given triangle IKL with vertices I(-1, 2), K(0, 3), and L(1, -1). The center of dilation is the origin (0,0) and the dilation rule is given by the transformation $(x, y) \to (5x, 5y)$. 2. **Formula and rules:** A dilation centered at the origin with scale factor $k$ transforms any point $(x, y)$ to $(kx, ky)$. 3. **Apply the dilation to each vertex:** - For vertex I(-1, 2): $$I' = (5 \times -1, 5 \times 2) = (-5, 10)$$ - For vertex K(0, 3): $$K' = (5 \times 0, 5 \times 3) = (0, 15)$$ - For vertex L(1, -1): $$L' = (5 \times 1, 5 \times -1) = (5, -5)$$ 4. **Final answer:** The vertices of the dilated image are: $$I' = (-5, 10), \quad K' = (0, 15), \quad L' = (5, -5)$$