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

1.	Let O(0, 0), P(3, 4), Q(6, 0) be the vertices of the triangle OPQ. The point R lies inside the ΔOPQ such that the triangles OPR, PQR, OQR 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)
Answer» Correct option (C) (3, 4/3) Explanation : A point inside a triangle divides the triangle into three triangles of equal areas if and only if the point is the centroid of the triangle. Hence, R must be the centroid of ΔOPQ. Therefore R(0 + 3 + 6/3 , 0 + 4 + 0/3) = (3,4/3)

Let O(0, 0), P(3, 4), Q(6, 0) be the vertices of the triangle OPQ. The point R lies inside the ΔOPQ such that the triangles OPR, PQR, OQR 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)

Answer»

Correct option (C) (3, 4/3)

Explanation :

A point inside a triangle divides the triangle into three triangles of equal areas if and only if the point is the centroid of the triangle. Hence, R must be the centroid of ΔOPQ. Therefore

R(0 + 3 + 6/3 , 0 + 4 + 0/3) = (3,4/3)

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Let O(0, 0), P(3, 4), Q(6, 0) be the vertices of the triangle OPQ. The point R lies inside the ΔOPQ such that the triangles OPR, PQR, OQR 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)

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