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

$(2, 2, 2)$

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$(3, 3, 3)$

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$(2, 2, 4)$

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$(3, 3, 4)$

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Solution

The correct option is D
$(3, 3, 4)$

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

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Similar questions

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

If a triangle has its orthocenter at (1, 1) and circumcenter at $(\frac{3}{2}, \frac{3}{4})$ , then the coordinates of the centroid of the triangle are

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

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

In an equilateral $△ A B C$ coordinates of the centroid of the triangle is ( $1, 2, 3)$ . Find the coordinates of the orthocenter of the triangle.

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

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