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ISRO 2014- Geometry [EE]

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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

(A) $(-1, 7/3)$

(B) $(-1/3, 7/3)$

(C) $(1, 7/3)$

(D) $(1/3, 7/3)$
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Let Co-ordinate of vertices be ABC given A(1,1) and mid point of AB & AC are (-1,2) & (3,2) respectively.

Mid point AB =(Xa + Xb)/2,(Ya + Yb)/2

hence -1=1+Xb /2  & 2=1+Yb /2

B(-3,3)

similarly

C(5,3)

centroid of Triangle is C(X,Y)= Xa+Xb+Xc/3, Ya+Yb+Yc/3

C(X,Y)=(1,7/3)

option C

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