Question

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

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

Answer 1

The correct option is C

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

Explanation of correct answer:

It is given that triangles $OPR,PQR,OQR$ are of equal area.

So, $R$ is the centroid of the triangle as centroid divide the traingle in $3$ equal areas. This means that,

$$\begin{gathered} \Rightarrow R\left(\frac{3+6+0}{3},\frac{4+0+0}{3}\right) \\ \Rightarrow R\left(3,\frac{4}{3}\right) \end{gathered}$$

Thus, the coordinates of $R$ are $\left(3,\frac{4}{3}\right)$.

Hence, option(C) is correct.