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:
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Official solution
Vertex of triangle is \[\left( {1,\,1} \right)\] and midpoint of sides through -
this vertex is \[\left( { - 1,\,2} \right)\] and \[\left( {3,2} \right)\]
\[ \Rightarrow \] vertex B and C come out to be \[\left( { - 3,3} \right)\] and \[\left( {5,3} \right)\]
\[\therefore\] centroid is \[{{1 - 3 + 5} \over 3},{{1 + 3 + 5} \over 3} \Rightarrow \left( {1,{7 \over 3}} \right)\]