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(C) The centroid $(G)$ of a triangle with vertices $(x_1, y_1, z_1)$,$(x_2, y_2, z_2)$,and $(x_3, y_3, z_3)$ is given by the formula $G = (\frac{x_1+x

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$-2, -8, 2$

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(C) The centroid $(G)$ of a triangle with vertices $(x_1, y_1, z_1)$,$(x_2, y_2, z_2)$,and $(x_3, y_3, z_3)$ is given by the formula $G = (\frac{x_1+x_2+x_3}{3}, \frac{y_1+y_2+y_3}{3}, \frac{z_1+z_2+z_3}{3})$.Given that the centroid is the origin $(0, 0, 0)$,we have:$\frac{a - 2 + 4}{3} = 0 \Rightarrow a + 2 = 0 \Rightarrow a = -2$.$\frac{1 + b + 7}{3} = 0 \Rightarrow b + 8 = 0 \Rightarrow b = -8$.$\frac{3 - 5 + c}{3} = 0 \Rightarrow c - 2 = 0 \Rightarrow c = 2$.Thus,the values are $a = -2, b = -8, c = 2$.

If the centroid of the triangle whose vertices are $(a, 1, 3)$,$(-2, b, -5)$,and $(4, 7, c)$ is the origin,then the values of $a, b, c$ are:

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