The midpoints of the sides of a triangle are | vedclass

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(B) The centroid of a triangle formed by joining the midpoints of the sides of another triangle is the same as the centroid of the original triangle.L

Vedclass · Accepted Answer

$(1, 4, 1/3)$

Vedclass · Answer

(B) The centroid of a triangle formed by joining the midpoints of the sides of another triangle is the same as the centroid of the original triangle.Let the midpoints be $M_1 = (1, 5, -1)$,$M_2 = (0, 4, -2)$,and $M_3 = (2, 3, 4)$.The centroid $G(x, y, z)$ of the triangle formed by these midpoints is given by the average of their coordinates:$x = \frac{1 + 0 + 2}{3} = \frac{3}{3} = 1$$y = \frac{5 + 4 + 3}{3} = \frac{12}{3} = 4$$z = \frac{-1 - 2 + 4}{3} = \frac{1}{3}$Therefore,the centroid is $(1, 4, 1/3)$.

The midpoints of the sides of a triangle are $(1, 5, -1)$,$(0, 4, -2)$,and $(2, 3, 4)$. Find the centroid of the triangle.

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