Let `O(0,0),P(3,4),` and `Q(6,0)` be the vertices of triangle `O P Q` . The point `R` inside the triangle `O P Q` is such that the triangles `O P R ,P Q R ,O Q R` are of equal area. The coordinates of `R` are a. `(4/3,3)` b. `(3,2/3)` c. `(3,4/3)` d. `(4/3,2/3)`

Options

A. (4/3,3)
B. (3,2/3)
C. (3,4/3)
D. (4/3,2/3)

Answer

C

Explanation

Clearly, `DeltaOPQ` is an isoscles triangle with OP=PQ. So, point R must coincide with the centroid of `DeltaOPQ`.

Hence, the coordinates of R are `((0+6+3)/(3),(0+0+4)/(3))=(3,(4)/(3))`