Q52 / 150 · MHT CET 2023 (12 May Shift 1) · Mathematics

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

  • Correct answer
    A
    $\left(\frac{3}{4}, \frac{-1}{4}, \frac{11}{4}\right)$
  • B
    $\left(\frac{5}{4}, \frac{-3}{4}, \frac{7}{4}\right)$
  • C
    $\left(\frac{-3}{4}, \frac{-1}{4}, \frac{11}{4}\right)$
  • D
    $\left(\frac{-5}{4}, \frac{-3}{4}, \frac{-7}{4}\right)$

Solution

Centroid of tetrahedron $$ \begin{aligned} & \equiv\left(\frac{-1+3+2-1}{4}, \frac{2-2+1-2}{4}, \frac{3+1+3+4}{4}\right) \\ & \equiv\left(\frac{3}{4}, \frac{-1}{4}, \frac{11}{4}\right) \end{aligned} $$

Hence, the correct answer is option: 'A'.

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