Let O(0,0), P(3,4) and Q(6,0) be the vertices of the O P Q . The point R inside the O P Q is such that the O P R, P Q R, O Q R are of equal area. The coordinates of R are

JEE Advanced 2007Paper 2

Exam: JEE Advanced
Year: 2007
Paper: Paper 2
Subject: Mathematics
Chapter: Properties of Triangles

JEE Advanced 2007 · Paper 2 · Mathematics · Properties of Triangles

Let O(0,0), P(3,4) and Q(6,0) be the vertices of the O P Q . The...

Let

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

and

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

\triangle O P R, \triangle P Q R, \triangle O Q R

are of equal area. The coordinates of

R

are

Let O(0,0), P(3,4) and Q(6,0) be the vertices of the O P Q . The point R inside the O P Q is such that the O P R, P Q

Options

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

Correct answer

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

Step-by-step solution

\text{ 7. Since, triangle is on isosceles, hence centroid is the desired point. } Let O(0,0), P(3,4) and Q(6,0) be the vertices of the O P Q . The point R inside the O P Q is such that the O P R, P Q

\\ \therefore

Coordinates of

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

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