The centroid of a triangle ABC is at the poin | vedclass

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(A) Let the coordinates of $C$ be $(x, y, z)$.Given that the centroid $G$ is $(1,1,1)$,and the vertices are $A(3,-5,7)$ and $B(-1,7,-6)$.The formula f

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$(1,1,2)$

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(A) Let the coordinates of $C$ be $(x, y, z)$.Given that the centroid $G$ is $(1,1,1)$,and the vertices are $A(3,-5,7)$ and $B(-1,7,-6)$.The formula for the centroid of a triangle is $G = (\frac{x_1+x_2+x_3}{3}, \frac{y_1+y_2+y_3}{3}, \frac{z_1+z_2+z_3}{3})$.Substituting the values,we get:$\frac{x+3-1}{3} = 1 \implies x+2 = 3 \implies x = 1$.$\frac{y-5+7}{3} = 1 \implies y+2 = 3 \implies y = 1$.$\frac{z+7-6}{3} = 1 \implies z+1 = 3 \implies z = 2$.Thus,the coordinates of point $C$ are $(1,1,2)$.

The centroid of a triangle $ABC$ is at the point $(1,1,1)$. If the coordinates of $A$ and $B$ are $(3,-5,7)$ and $(-1,7,-6)$ respectively,find the coordinates of the point $C$.

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