Four vertices of a tetrahedron are $(0, 0, 0), (4, 0, 0), (0, - 8, 0)$ and $(0, 0, 12)$ . Its centroid has the coordinates

(\frac{4}{3}, - \frac{8}{3}, 4)

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(2, - 4, 6)

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(1, - 2, 3)

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none of these

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Solution

The correct option is C $(1, - 2, 3)$
If the vertices of tetrahedron are, $(x_{1}, y_{1}, z_{1}), (x_{2}, y_{2}, z_{2}), (x_{3}, y_{3}, z_{3}), (x_{4}, y_{4}, z_{4})$ , then the centroid of tetrahedron is
$(\frac{x_{1} + x_{2} + x_{3} + x_{4}}{4}, \frac{y_{1} + y_{2} + y_{3} + y_{4}}{4}, \frac{z_{1} + z_{2} + z_{3} + z_{4}}{4})$
Thus from the vertices given in the question, the centroid is
$= (\frac{4}{4}, \frac{- 8}{4}, \frac{12}{4})$
$= (1, - 2, 3)$

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