Triangle Enlargement 4Ab11C

1. **Problem Statement:** We need to enlarge the triangle with vertices at $(2,4)$, $(2,5)$, and $(4,5)$ by a scale factor of $-3$ centered at the point $(2,3)$. 2. **Formula for enlargement:** If a point $P=(x,y)$ is enlarged by scale factor $k$ about center $C=(x_c,y_c)$, the new point $P'=(x',y')$ is given by: $$ x' = x_c + k(x - x_c), \quad y' = y_c + k(y - y_c) $$ 3. **Apply the formula to each vertex:** - For $A=(2,4)$: $$ x'_A = 2 + (-3)(2 - 2) = 2 + (-3)(0) = 2$$ $$ y'_A = 3 + (-3)(4 - 3) = 3 + (-3)(1) = 3 - 3 = 0$$ So, $A' = (2,0)$. - For $B=(2,5)$: $$ x'_B = 2 + (-3)(2 - 2) = 2 + 0 = 2$$ $$ y'_B = 3 + (-3)(5 - 3) = 3 + (-3)(2) = 3 - 6 = -3$$ So, $B' = (2,-3)$. - For $C=(4,5)$: $$ x'_C = 2 + (-3)(4 - 2) = 2 + (-3)(2) = 2 - 6 = -4$$ $$ y'_C = 3 + (-3)(5 - 3) = 3 + (-3)(2) = 3 - 6 = -3$$ So, $C' = (-4,-3)$. 4. **Summary of new vertices:** The enlarged triangle has vertices at: $$ A' = (2,0), \quad B' = (2,-3), \quad C' = (-4,-3) $$ 5. **Interpretation:** The triangle is scaled by a factor of $-3$ about $(2,3)$, which means it is enlarged by 3 times and reflected through the center point. **Final answer:** The vertices of the enlarged triangle are $(2,0)$, $(2,-3)$, and $(-4,-3)$.