Question

Prove using vectors the mid-points of two opposite sides of a quadrilateral and the midpoints of the diagonals are the vertices of a parallelogram.

Answer 1

ABCD is a quadrilateral with position vectors 

OA = vector a, OB = vector b, OC = vector c and OD = vector d 

P is the midpoint of BC and R is the midpoint of AD. 

Q is the midpoint of AC and S is the midpoint of BD. 

To prove PQRS is a parallelogram. We have to prove that vector PQ = vector SR

Now