The centroid of a tetrahedron with vertices A | vedclass

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(B) 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 formul

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$6$

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(B) 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: $G = \left( \frac{x_1+x_2+x_3+x_4}{4}, \frac{y_1+y_2+y_3+y_4}{4}, \frac{z_1+z_2+z_3+z_4}{4} \right)$ Given the vertices $A(3, -5, x)$,$B(5, 4, 2)$,$C(7, -7, y)$,$D(1, 0, z)$ and centroid $G(4, -2, 2)$,we equate the coordinates: For the $z$-coordinate: $\frac{x + 2 + y + z}{4} = 2$ $x + y + z + 2 = 8$ $x + y + z = 8 - 2$ $x + y + z = 6$

The centroid of a tetrahedron with vertices $A(3, -5, x)$,$B(5, 4, 2)$,$C(7, -7, y)$,and $D(1, 0, z)$ is $G(4, -2, 2)$. Then,the value of $x + y + z$ is:

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