JEE Advanced · 2007 · 08 Apr 2007 · Paper 2 · Straight Lines

Let

O (0, 0), P (3, 4), Q (6, 0)

be the vertices of the triangle

O P Q

. The point

R

inside the triangle

O P Q

is such that the triangles

O P R, P QR, O QR

are of equal area. The coordinates of

R

are

(A) $(\frac{4}{3}, 3)$
(B) $(3, \frac{2}{3})$
(C) $(3, \frac{4}{3})$ ✓ Correct
(D) $(\frac{4}{3}, \frac{2}{3})$

Answer: (C)

Solution

Since the triangle

O P Q

is isosceles (with

O P = 5

and

O Q = 6

, and

P Q = 5

), and the three sub-triangles

O P R, P QR, O QR

have equal areas, the point

R

must be the centroid of triangle

O P Q

. The centroid is given by

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

JEE Advanced · 2007 · 08 Apr 2007 · Paper 2 · Single correct option

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