The centroid of a triangle is (2, 7) and two | vedclass

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Question

(B) Let the third vertex be $(x, y)$.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 give

Vedclass · Accepted Answer

$(4, 7)$

Vedclass · Answer

(B) Let the third vertex be $(x, y)$.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 given by $G = (\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3})$.Given $G = (2, 7)$,$(x_1, y_1) = (4, 8)$,and $(x_2, y_2) = (-2, 6)$.For the $x$-coordinate: $\frac{4 + (-2) + x}{3} = 2$ $\Rightarrow 2 + x = 6$ $\Rightarrow x = 4$.For the $y$-coordinate: $\frac{8 + 6 + y}{3} = 7$ $\Rightarrow 14 + y = 21$ $\Rightarrow y = 7$.Therefore,the third vertex is $(4, 7)$.

The centroid of a triangle is $(2, 7)$ and two of its vertices are $(4, 8)$ and $(-2, 6)$. The third vertex is

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