The centroid of a tetrahedron with vertices a | vedclass

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Question

(A) The centroid $(G)$ of a tetrahedron with vertices $(x_1, y_1, z_1)$,$(x_2, y_2, z_2)$,$(x_3, y_3, z_3)$,and $(x_4, y_4, z_4)$ is given by the form

Vedclass · Accepted Answer

$\left(\frac{3}{4}, \frac{-1}{4}, \frac{11}{4}\right)$

Vedclass · Answer

(A) The centroid $(G)$ of a tetrahedron with vertices $(x_1, y_1, z_1)$,$(x_2, y_2, z_2)$,$(x_3, y_3, z_3)$,and $(x_4, y_4, z_4)$ is given by the formula: $G = \left(\frac{x_1+x_2+x_3+x_4}{4}, \frac{y_1+y_2+y_3+y_4}{4}, \frac{z_1+z_2+z_3+z_4}{4}\right)$ Substituting the given coordinates $A(-1, 2, 3)$,$B(3, -2, 1)$,$C(2, 1, 3)$,and $D(-1, -2, 4)$: $G = \left(\frac{-1+3+2-1}{4}, \frac{2-2+1-2}{4}, \frac{3+1+3+4}{4}\right)$ $G = \left(\frac{3}{4}, \frac{-1}{4}, \frac{11}{4}\right)$ Thus,the correct option is $A$.

The centroid of a tetrahedron with vertices at $A(-1, 2, 3)$,$B(3, -2, 1)$,$C(2, 1, 3)$,and $D(-1, -2, 4)$ is:

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