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Question: Answered & Verified by Expert
If the orthocenter and circumcenter of a triangle respectively are $(3,-4,2)$ and $(2,1,3)$, then its centroid is
MathematicsStraight LinesAP EAMCETAP EAMCET 2021 (24 Aug Shift 2)
Options:
  • A $\left(\frac{-7}{3}, \frac{6}{3}, \frac{-4}{3}\right)$
  • B $\left(\frac{7}{3}, \frac{-6}{3}, \frac{4}{3}\right)$
  • C $\left(\frac{7}{3}, \frac{-6}{3}, \frac{-4}{3}\right)$
  • D $\left(\frac{7}{3}, \frac{-2}{3}, \frac{8}{3}\right)$
Solution:
2793 Upvotes Verified Answer
The correct answer is: $\left(\frac{7}{3}, \frac{-2}{3}, \frac{8}{3}\right)$
Given, orthocentre and circumcentre of triangle are $(3,-4,2)$ and $(2,1,3)$ respectively We know that centroid of triangle is divide orthocentre and circumcentre in the ratio $2: 1$.
$\therefore$ Centroid of triangle is
$\left(\frac{3+2(2)}{3}, \frac{-4+2(1)}{3}, \frac{2+2(3)}{3}\right)$
i.e., $\left(\frac{7}{3}, \frac{-2}{3}, \frac{8}{3}\right)$

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