Prove that the line segments joining the midpoints of opposite sides of a quadrilateral bisect each other.

Question

solve it by vector method plz

Answer 1

Quadrilateral ABCD, going clockwise from upper left.

 

A(x1,y1)

B(x2,y2)

C(x3,y3)

D(x4,y4)

 

midpoint of AB is (X1+x2)/2, (y1+y2)/2

midpoint of CD is (x3+x4)/2, (y3+y4)/2

midpoint of AD is (x1+x3)/2. (y1+y3)/2

midpoint of BC is (x2+x3)/2, (y2+y3)/2

 

The midpoints of both bisectors are indeed  (x1+x2+x3+x4)/2  ,  (y1+y2+y3+y4)/2

 

end of proof