Let a → , b → , c → be the position vectors of the vertices of a triangle A B C . Through the vertices, lines are drawn parallel to the sides to form the triangle A ' B ' C ' . Then the centroid of Δ A ' B ' C ' is

Step-by-step solution

Here, A is mid-point of B ' C ' , B is mid-point of A ' C ' and C is mid-point of A ' B ' . By mid-point formula a → = b ' → + c ' → 2 ,   b → = a ' → + c ' → 2 ,   c → = b ' → + a ' → 2 Centroid of triangle A B C , G = a → + b → + c → 3 = b ' → + c ' → 2 + a ' → + c ' → 2 + b ' → + a ' → 2 3 = a ' → + b ' →