The centroid of a triangle is (2, 3) and two | vedclass

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(A) Let the vertices of the triangle be $A(5, 6)$,$B(-1, 4)$,and $C(x, y)$.Given that the centroid $G$ is $(2, 3)$.The formula for the centroid of a t

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$(2, -1)$

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(A) Let the vertices of the triangle be $A(5, 6)$,$B(-1, 4)$,and $C(x, y)$.Given that the centroid $G$ is $(2, 3)$.The formula for the centroid of a triangle with vertices $(x_1, y_1)$,$(x_2, y_2)$,and $(x_3, y_3)$ is given by $G = (\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3})$.Substituting the given values:$2 = \frac{5 + (-1) + x}{3} \implies 6 = 4 + x \implies x = 2$.$3 = \frac{6 + 4 + y}{3} \implies 9 = 10 + y \implies y = -1$.Thus,the third vertex is $(2, -1)$.

The centroid of a triangle is $(2, 3)$ and two of its vertices are $(5, 6)$ and $(-1, 4)$. Find the third vertex of the triangle.

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