Question

Let O(0, 0), P(3, 4) and Q(6, 0) be the vertices of a triangle OPQ. A point R is inside the triangle such that the triangles OPR, PQR and OQR are of equal areas. Then, then,the coordinate of R are

(A)  (4/3,3)

(B)  (3,2/3)

(C)  (3,4/3)

(D)  (2/3,4/3)

Answer 1

Correct option  (c)  (3,4/3)

Explanation :

Let  ΔABC be any triangle. P is an inside point such that the triangles PBC, PCA and PAB are of equal areas if and only if P is the centroid of ΔABC. Hence, R must be the centroid of ΔOPQ and so

R = (3,4/3)