Question

Prove that the straight lines joining the mid points of the sides of a quadrilateral ABCD, taken in order, form a parallelogram.

Answer 1

Let the position vectors of A, B, C and D be vector(a, b, c) and  vector d. Hence position vectors of P, Q, R and S (the mid points of AB, BC, CD & DA respectively) are

Vector PQ  is parallel and equal to Vector SR. 

Hence PQRS is a parallelogram.