If the orthocenter and circumcenter of a triangle respectively are $(3,-4,2)$ and $(2,1,3)$, then its…

If the orthocenter and circumcenter of a triangle respectively are $(3,-4,2)$ and $(2,1,3)$, then its centroid is
  1. $\left(\frac{-7}{3}, \frac{6}{3}, \frac{-4}{3}\right)$
  2. $\left(\frac{7}{3}, \frac{-6}{3}, \frac{4}{3}\right)$
  3. $\left(\frac{7}{3}, \frac{-6}{3}, \frac{-4}{3}\right)$
  4. $\left(\frac{7}{3}, \frac{-2}{3}, \frac{8}{3}\right)$

Solution

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., $\left(\frac{7}{3}, \frac{-2}{3}, \frac{8}{3}\right)$

Asked in: AP EAMCET 2021 (24 Aug Shift 2)

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