IIT-JEE 2007 · Paper 2 · Mathematics Q45

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MathematicsSingle correct+3 / -1Question 45 of 66

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

\left(\frac43,3\right)

\left(3,\frac23\right)

\left(3,\frac43\right)

\left(\frac43,\frac23\right)

Answer and worked solution

Official answer: C

Equal areas means centroid. The centroid G splits a triangle into three triangles of equal area (each $\frac13$ of the whole), and it is the only interior point that does.

So $R=\left(\dfrac{0+3+6}3,\dfrac{0+4+0}3\right)=\left(3,\dfrac43\right)$ .

(C)

Topics:Distance and section formulae

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IIT-JEE 2007 · Paper 2, Mathematics question 45