Question

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

The correct option is C $(3,\frac{4}{3})$

$\because Ar\left(\Delta OPR\right)=Ar\left(\Delta PQR\right)=Ar\left(\Delta OQR\right)$


$\therefore$ By simply geometry,
R should be the centroid of $\Delta PQO$
$\Rightarrow R(\frac{3+6+0}{3},\frac{4+0+0}{3})=(3,\frac{4}{3})$