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Nasty vector question

  1. Feb 21, 2006 #1
    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
     
  2. jcsd
  3. Feb 21, 2006 #2

    benorin

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    Homework Helper

    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
     
    Last edited: Feb 21, 2006
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