Triangle Enlargement 7Cf4B9

1. **State the problem:** We need to enlarge a triangle with vertices at $(7,9)$, $(7,7)$, and $(8,7)$ by a scale factor of $-2$ with the centre of enlargement at $(6,6)$. 2. **Formula for enlargement:** If the centre of enlargement is $C(x_c,y_c)$ and a point $P(x,y)$ is enlarged by scale factor $k$, the new point $P'(x',y')$ is given by: $$x' = x_c + k(x - x_c)$$ $$y' = y_c + k(y - y_c)$$ 3. **Apply the formula to each vertex:** - For $A(7,9)$: $$x' = 6 + (-2)(7 - 6) = 6 + (-2)(1) = 6 - 2 = 4$$ $$y' = 6 + (-2)(9 - 6) = 6 + (-2)(3) = 6 - 6 = 0$$ - For $B(7,7)$: $$x' = 6 + (-2)(7 - 6) = 6 - 2 = 4$$ $$y' = 6 + (-2)(7 - 6) = 6 + (-2)(1) = 6 - 2 = 4$$ - For $C(8,7)$: $$x' = 6 + (-2)(8 - 6) = 6 + (-2)(2) = 6 - 4 = 2$$ $$y' = 6 + (-2)(7 - 6) = 6 - 2 = 4$$ 4. **Final enlarged vertices:** The enlarged triangle has vertices at $(4,0)$, $(4,4)$, and $(2,4)$. 5. **Interpretation:** The negative scale factor means the triangle is reflected through the centre of enlargement and scaled by a factor of $2$. The triangle is now larger and positioned accordingly. **Answer:** The enlarged triangle vertices are $(4,0)$, $(4,4)$, and $(2,4)$.