If (1,0,3), (2,1,5), (-2,3,6) are the mid-poi | vedclass

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(B) Let the mid-points of the sides of $	riangle ABC$ be $D(1,0,3)$,$E(2,1,5)$,and $F(-2,3,6)$.The centroid of the triangle formed by the mid-points

Vedclass · Accepted Answer

$\left(\frac{1}{3}, \frac{4}{3}, \frac{14}{3}\right)$

Vedclass · Answer

(B) Let the mid-points of the sides of $	riangle ABC$ be $D(1,0,3)$,$E(2,1,5)$,and $F(-2,3,6)$.The centroid of the triangle formed by the mid-points of the sides of a triangle is the same as the centroid of the original triangle.Therefore,the centroid of $	riangle ABC$ is the same as the centroid of $	riangle DEF$.The formula for the centroid of a triangle with vertices $(x_1, y_1, z_1), (x_2, y_2, z_2), (x_3, y_3, z_3)$ is $\left(\frac{x_1+x_2+x_3}{3}, \frac{y_1+y_2+y_3}{3}, \frac{z_1+z_2+z_3}{3}ight)$.Substituting the given mid-points:Centroid $= \left(\frac{1+2-2}{3}, \frac{0+1+3}{3}, \frac{3+5+6}{3}ight)$$= \left(\frac{1}{3}, \frac{4}{3}, \frac{14}{3}ight)$.

If $(1,0,3), (2,1,5), (-2,3,6)$ are the mid-points of the sides of a triangle,then the centroid of the triangle is

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