Q.

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

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a

(4/3,3)

b

(3,2/3)

c

(3,4/3)

d

(4/3,2/3)

answer is C.

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Detailed Solution

Ar⁡(ΔOPR)=Ar⁡(ΔPQR)=Ar⁡(ΔOQR)R should be the centroid of △PQO whose coordinates are3+6+03,4+0+03≡3,43
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Let O(0, 0), P(3, 4), and Q(6,0) be the vertices of 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