Question

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

• A. $(\frac{4}{3},3)$
• B. $(3,\frac{2}{3})$
• C. $(3,\frac{4}{3})$
• D. $(\frac{4}{3},\frac{2}{3})$

Answer 1

Answer: (C)

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

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.

We need to find the coordinates of $R$.

Since the triangle is isoceles, centroid represents the coordinate of $R$.

$R=(\frac{0+3+6}{3},\frac{0+4+0}{3})$

$\Rightarrow R=(\frac{9}{3},\frac{4}{3})$

$\therefore R=(3,\frac{4}{3})$