Two vertices of the triangle are (3, 1) and ( | vedclass

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(B) Let the vertices of the triangle be $A(3, 1)$,$B(1, 5)$,and $C(x, y)$.The centroid $G$ of a triangle with vertices $(x_1, y_1)$,$(x_2, y_2)$,and $

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$(-4, -6)$

Vedclass · Answer

(B) Let the vertices of the triangle be $A(3, 1)$,$B(1, 5)$,and $C(x, y)$.The centroid $G$ of a triangle with vertices $(x_1, y_1)$,$(x_2, y_2)$,and $(x_3, y_3)$ is given by the formula $G = \left( \frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3} \right)$.Given that the centroid $G$ is the origin $(0, 0)$,we have:$\frac{3 + 1 + x}{3} = 0 \implies 4 + x = 0 \implies x = -4$.$\frac{1 + 5 + y}{3} = 0 \implies 6 + y = 0 \implies y = -6$.Therefore,the third vertex is $(-4, -6)$.

Two vertices of the triangle are $(3, 1)$ and $(1, 5)$. If the centroid of the triangle is the origin,then the third vertex is:

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