(C) point $R$ inside a triangle $OPQ$ such that the areas of triangles $OPR, PQR, OQR$ are equal is the centroid of the triangle.Given the vertices $O

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(C) point $R$ inside a triangle $OPQ$ such that the areas of triangles $OPR, PQR, OQR$ are equal is the centroid of the triangle.Given the vertices $O(0,0), P(3,4), Q(6,0)$,the coordinates of the centroid $R(x, y)$ are given by:$x = \frac{x_1 + x_2 + x_3}{3} = \frac{0 + 3 + 6}{3} = \frac{9}{3} = 3$$y = \frac{y_1 + y_2 + y_3}{3} = \frac{0 + 4 + 0}{3} = \frac{4}{3}$Thus,the coordinates of $R$ are $\left(3, \frac{4}{3}\right)$.

Class 11 Mathematics Straight Line Points related to triangle

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Let $O(0,0), P(3,4), Q(6,0)$ be the vertices of the triangle $OPQ$. The point $R$ inside the triangle $OPQ$ is such that the triangles $OPR, PQR, OQR$ are of equal area. The coordinates of $R$ are

IIT 2007 All IIT

A
$\left(\frac{4}{3}, 3\right)$
B
$\left(3, \frac{2}{3}\right)$
C
$\left(3, \frac{4}{3}\right)$
D
$\left(\frac{4}{3}, 2\right)$

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Let $O(0,0), P(3,4), Q(6,0)$ be the vertices of the triangle $OPQ$. The point $R$ inside the triangle $OPQ$ is such that the triangles $OPR, PQR, OQR$ are of equal area. The coordinates of $R$ are

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