1. **Problem Statement:** Find the coordinates of the images of vertices B, C, and D of triangle △BCD under a dilation centered at the origin with scale factor 3. 2. **Formula and Explanation:** A dilation centered at the origin with scale factor $k$ transforms any point $(x,y)$ to $(kx, ky)$. 3. **Given Points:** - $B = (1, -3)$ - $C = (2, -1)$ - $D = (3, 3)$ 4. **Apply Dilation:** - Image of $B$: $(3 \times 1, 3 \times -3) = (3, -9)$ - Image of $C$: $(3 \times 2, 3 \times -1) = (6, -3)$ - Image of $D$: $(3 \times 3, 3 \times 3) = (9, 9)$ 5. **Explanation:** Each coordinate is multiplied by the scale factor 3 because the dilation is centered at the origin, which means distances from the origin are scaled by 3. **Final answer:** - $B' = (3, -9)$ - $C' = (6, -3)$ - $D' = (9, 9)$