Proving the Midpoint Theorem for a Plane Quadrilateral | Helpful Tips

[Superdreamer]

Please Help! nasty vector question

The diagonals of a plane quadrilateral ABCD intersect at O,and X,Y are the midpoints of the diagonals AC,BD respectively.Show that
The shape is not regular the top and bottom are different lengths as can be the sides

1) BA + BC= 2BX
Got this part by proving
BA=BX+XA
BC=BX+XC
BA+BC=BX+XA+BX+XC
2BX+XA+XC
2BX-1/2AC+1/2AC=BA+BC
From here on in I just go blank
I've tried proving no 2 by getting DA=DX+XA OR DY+YA etc but it ain't working

2) BA + BC +DA + DC=4YX
3) 2AB +_2BC +2CA=0
iF 0A+OB+OC+OD=4OM find location of M

Thanks in advance

 

[benorin]

Perhaps it would help to consider that

YX=YA+AX
YX=YB+BX
YX=YC+CX
YX=YD+DX

their sum is

4YX=AX+BX+CX+DX+YA+YB+YC+YD

since AX+CX=0 and YB+YD=0, we have

4YX=BX+DX+YA+YC