question_answer

If a vertex of a triangle is (1, 1) and the mid points of two sides through this vertex are (-1, 2) and (3, 2), then the centroid of the triangle is   [AIEEE 2005]

A) \[\left( 1,\,\frac{7}{3} \right)\]

B) \[\left( \frac{1}{3},\,\frac{7}{3} \right)\]

C) \[\left( -1,\,\frac{7}{3} \right)\]

D) \[\left( \frac{-1}{3},\,\frac{7}{3} \right)\]

Correct Answer: A

Solution :

Vertex of triangle is (1, 1) and midpoint of sides through this vertex is (-1, 2) and (3, 2) Þ Vertex B and C come out to be (-3, 3) and (5, 3) \ Centroid is \[\left( \frac{1-3+5}{3},\frac{1+3+3}{3} \right)=(1,7/3)\]