O(0, 0), P(3, 4), Q(6, 0) are the vertices of | vedclass

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(C) Let the coordinates of $R$ be $(a, b)$.Since the areas of triangles $OPR, PQR,$ and $OQR$ are equal,the point $R$ is the centroid of the triangle

Vedclass · Accepted Answer

$\left( 3, \frac{4}{3} \right)$

Vedclass · Answer

(C) Let the coordinates of $R$ be $(a, b)$.Since the areas of triangles $OPR, PQR,$ and $OQR$ are equal,the point $R$ is the centroid of the triangle $OPQ$.The coordinates of the centroid $(a, b)$ of a triangle with vertices $(x_1, y_1), (x_2, y_2),$ and $(x_3, y_3)$ are given by $\left( \frac{x_1+x_2+x_3}{3}, \frac{y_1+y_2+y_3}{3} \right)$.Substituting the given vertices $O(0, 0), P(3, 4),$ and $Q(6, 0)$:$a = \frac{0+3+6}{3} = \frac{9}{3} = 3$$b = \frac{0+4+0}{3} = \frac{4}{3}$Therefore,the coordinates of $R$ are $\left( 3, \frac{4}{3} \right)$.

$O(0, 0), P(3, 4), Q(6, 0)$ are the vertices of a triangle $OPQ$. $A$ point $R$ lies inside the triangle $OPQ$ such that the areas of triangles $OPR, PQR,$ and $OQR$ are equal. Find the coordinates of $R$.

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