Find the centroid of a triangle,the mid-point | vedclass

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(A) Let the vertices of the triangle be $A(x_1, y_1, z_1)$,$B(x_2, y_2, z_2)$,and $C(x_3, y_3, z_3)$.The mid-points of the sides are given as $D(1, 2,

Vedclass · Accepted Answer

$G(1, 1, -2)$

Vedclass · Answer

(A) Let the vertices of the triangle be $A(x_1, y_1, z_1)$,$B(x_2, y_2, z_2)$,and $C(x_3, y_3, z_3)$.The mid-points of the sides are given as $D(1, 2, -3)$,$E(3, 0, 1)$,and $F(-1, 1, -4)$.We know that 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.The centroid $G(x, y, z)$ of $\Delta DEF$ is calculated as:$x = \frac{1 + 3 + (-1)}{3} = \frac{3}{3} = 1$$y = \frac{2 + 0 + 1}{3} = \frac{3}{3} = 1$$z = \frac{-3 + 1 + (-4)}{3} = \frac{-6}{3} = -2$Therefore,the centroid of the triangle is $G(1, 1, -2)$.

Find the centroid of a triangle,the mid-points of whose sides are $D(1, 2, -3)$,$E(3, 0, 1)$,and $F(-1, 1, -4)$.

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