Question

Prove that the lines joining the middle points of the opposite sides of a quadrilateral and the join of the middle points of its diagonals meet in a point and bisect one another.

Answer 1

Let OBCD be the quadrilateral P,Q,R, S be the midpoint off OB,CD,OD and BC.

Let the coordinates of O,B,C,D are (0,0), (x,0), (x,y), (0,y)

Coordinates of midpoint of PQ are

Coordinates of midpoint of RS are

Since, the coordinates of the mid-point of PQ = coordinates of mid-point of RS

Therefore, PQ and RS bisect each other