Two vertices of a triangle are (5, 4) and (-2 | vedclass

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(A) Let the third vertex be $(x, y)$.Given that the centroid of the triangle is $(5, 6)$.The formula for the centroid $(G)$ of a triangle with vertice

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$(12, 10)$

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(A) Let the third vertex be $(x, y)$.Given that the centroid of the triangle is $(5, 6)$.The formula for the centroid $(G)$ of a triangle with vertices $(x_1, y_1)$,$(x_2, y_2)$,and $(x_3, y_3)$ is $G = (\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3})$.Substituting the given values: $5 = \frac{5 - 2 + x}{3}$ and $6 = \frac{4 + 4 + y}{3}$.For the $x$-coordinate: $15 = 3 + x \Rightarrow x = 12$.For the $y$-coordinate: $18 = 8 + y \Rightarrow y = 10$.Therefore,the third vertex is $(12, 10)$.

Two vertices of a triangle are $(5, 4)$ and $(-2, 4)$. If its centroid is $(5, 6)$,then the third vertex has the coordinates:

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