1. **Stating the problem:** We have a triangle $\triangle ABC$ and we want to find the image of this triangle after an enlargement with center of enlargement at $(2,-1)$ and scale factor 2. 2. **Formula for enlargement:** If $P(x,y)$ is a point and $C(x_c,y_c)$ is the center of enlargement with scale factor $k$, the image point $P'(x',y')$ is given by: $$x' = x_c + k(x - x_c)$$ $$y' = y_c + k(y - y_c)$$ 3. **Explanation:** This means we measure the vector from the center to the point, multiply it by the scale factor, and then add it back to the center coordinates. 4. **Apply to each vertex:** Let the vertices of $\triangle ABC$ be $A(x_A,y_A)$, $B(x_B,y_B)$, and $C(x_C,y_C)$. We calculate each image vertex $A'$, $B'$, and $C'$ using the formula. 5. **Example:** Suppose the vertices are $A(1,2)$, $B(3,4)$, and $C(5,0)$ (you can replace these with actual vertices if given). Calculate $A'$: $$x' = 2 + 2(1 - 2) = 2 + 2(-1) = 2 - 2 = 0$$ $$y' = -1 + 2(2 + 1) = -1 + 2(3) = -1 + 6 = 5$$ Calculate $B'$: $$x' = 2 + 2(3 - 2) = 2 + 2(1) = 2 + 2 = 4$$ $$y' = -1 + 2(4 + 1) = -1 + 2(5) = -1 + 10 = 9$$ Calculate $C'$: $$x' = 2 + 2(5 - 2) = 2 + 2(3) = 2 + 6 = 8$$ $$y' = -1 + 2(0 + 1) = -1 + 2(1) = -1 + 2 = 1$$ 6. **Result:** The image triangle $\triangle A'B'C'$ has vertices $A'(0,5)$, $B'(4,9)$, and $C'(8,1)$. 7. **Graphing:** Both the original and image triangles can be plotted on the same coordinate plane to visualize the enlargement. This completes the enlargement process.