Question
Show that the lines joining the mid-points of the opposite sides of a quadrilateral bisect each other.
Solution
Let 
be position vectors of vertices A, B, C, D of quadrilateral ABCD.
Let P, Q, R, S be mid-points of the sides AB, BC, CD, DA respectively of quadrilateral ABCD.
position vectors of P, Q, R, S are
respectively.
Position vectors of mid - point of PR is
Position vector of mid- point of QS is
Since position vector of mid-points of PR and QS is same.
∴ lines joining the mid-points of the opposite sides of a quadrilateral bisect each other.
