Two vertices of a triangle are (3, -5) and (- | vedclass

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(D) Let the vertices of the triangle be $A(3, -5)$,$B(-7, 4)$,and $C(x, y)$.The centroid $G(x_g, y_g)$ of a triangle with vertices $(x_1, y_1)$,$(x_2,

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$(10, -2)$

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(D) Let the vertices of the triangle be $A(3, -5)$,$B(-7, 4)$,and $C(x, y)$.The centroid $G(x_g, y_g)$ of a triangle with vertices $(x_1, y_1)$,$(x_2, y_2)$,and $(x_3, y_3)$ is given by the formula:$x_g = \frac{x_1 + x_2 + x_3}{3}$ and $y_g = \frac{y_1 + y_2 + y_3}{3}$.Given $G = (2, -1)$,we have:$2 = \frac{3 + (-7) + x}{3} \implies 6 = -4 + x \implies x = 10$.$-1 = \frac{-5 + 4 + y}{3} \implies -3 = -1 + y \implies y = -2$.Thus,the coordinates of the third vertex are $(10, -2)$.

Two vertices of a triangle are $(3, -5)$ and $(-7, 4)$. If the centroid of the triangle is $(2, -1)$,then find the coordinates of the third vertex.

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