The two vertices of a triangle are (-1, 4) an | vedclass

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(D) Let the third vertex be $(x, y)$.The coordinates of the centroid of a triangle with vertices $(x_1, y_1), (x_2, y_2), (x_3, y_3)$ are given by $\l

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$(-4, -15)$

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(D) Let the third vertex be $(x, y)$.The coordinates of the centroid of a triangle with vertices $(x_1, y_1), (x_2, y_2), (x_3, y_3)$ are given by $\left( \frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3} \right)$.Given the vertices $(-1, 4)$ and $(5, 2)$,the centroid is $\left( \frac{-1 + 5 + x}{3}, \frac{4 + 2 + y}{3} \right) = \left( \frac{4 + x}{3}, \frac{6 + y}{3} \right)$.Equating this to the given centroid $(0, -3)$:$\frac{4 + x}{3} = 0$ $\Rightarrow 4 + x = 0$ $\Rightarrow x = -4$.$\frac{6 + y}{3} = -3$ $\Rightarrow 6 + y = -9$ $\Rightarrow y = -15$.Thus,the third vertex is $(-4, -15)$.

The two vertices of a triangle are $(-1, 4)$ and $(5, 2)$. If its centroid is $(0, -3)$,find the third vertex.

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