JEE Advanced 2007 Paper 2Question 1
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
Points and Straight Lines
Solution
Equal areas $\Rightarrow$ $R$ is the centroid: $\left(\frac{0+3+6}3,\frac{0+4+0}3\right)=\left(3,\frac43\right)$.