1. **State the problem:** We have triangle ABC with vertices A(-3, -2), B(0, 4), and C(4, 1). We want to find the coordinates of the triangle after two transformations: - Dilate by a factor of 2 centered at the origin. - Reflect across the x-axis. 2. **Dilate by a factor of 2 centered at the origin:** The dilation formula for a point $(x,y)$ with center at the origin and scale factor $k$ is: $$ (x', y') = (kx, ky) $$ Applying this to each vertex with $k=2$: - $A' = (2 \times -3, 2 \times -2) = (-6, -4)$ - $B' = (2 \times 0, 2 \times 4) = (0, 8)$ - $C' = (2 \times 4, 2 \times 1) = (8, 2)$ 3. **Reflect across the x-axis:** Reflection across the x-axis changes a point $(x,y)$ to $(x, -y)$. Applying this to each dilated vertex: - $A'' = (-6, -(-4)) = (-6, 4)$ - $B'' = (0, -8)$ - $C'' = (8, -2)$ 4. **Final coordinates:** The vertices of the transformed triangle are: $$ A''(-6, 4), B''(0, -8), C''(8, -2) $$ This completes the transformations and gives the final triangle coordinates.