In a triangle coordinates of orthocenter and circumcenter are $(- 3, 5, 2)$ and $(6, 2, 5)$ . Find the coordinates of centroid of the triangle.

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Solution

The correct option is D

Orthocenter, centroid and circumcenter are colliner for any triangle

and for equilateral triangle these three points are same.

Centroid divides orthocenter $&$ circumcenter in the ratio of 2:1.

Coordinates of the centroid of the triangle

$G (\frac{m x_{2} + n x_{1}}{m + n}, \frac{m y_{2} + n y_{1}}{m + n}, \frac{m z_{2} + n z_{1}}{m + n})$ where m:n =2:1

$G (\frac{2 (6) + 1 (- 3)}{2 + 1}, \frac{2 (2) + 1 (5)}{2 + 1}, \frac{2 (5) + 1 (2)}{2 + 1})$

$G (\frac{12 - 3}{3}, \frac{4 + 5}{3}, \frac{10 + 2}{3})$

$G (3, 3, 4)$

Option D is correct

Suggest Corrections

Similar questions

(1, 1)

(\frac{3}{2}, \frac{3}{4})

Which of the following statements are correct?

1. For triangle orthocenter,circumcenter and

centroid are collinear.

2. Centroid divides the line joining the circumcenter $&$ orthocenter

in the ratio of $2 : 1$ i.e., $\frac{C S}{O C} = \frac{2}{1}$

Where C-Coordinate of centroid

O-Coordinate of orthocenter

S--Coordinate of circumcenter