Question
The mid-points of two opposite sides of a quadrilateral and the mid-points of the diagonals are the vertices of a parallelogram. Prove using vectors.
Solution
Let 
be position vectors of vertices A, B, C, D respectively.
Let E, F, G, H be mid-points of AB, CD, AC, BD respectively.
P.V. of E = 
P.V. of F = 
