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Math Help - Math game with transformations

  1. #1
    Newbie
    Joined
    Feb 2008
    Posts
    3

    Math game with transformations

    Hi, I really need your help. My Maths teacher wants me to do a presentation on the follwoing problem to improve my Maths mark. I just don't know how to do that task. Please help me.

    There are 4 points on a plane coordinate system.
    These points have the following coordinates:
    1.(0;0)
    2.(1;0)
    3.(0;1)
    4.(1;1)
    These 4 points are to be repositioned.
    You may only reposition points in the following way:
    You may only change the position of a point, if there is another
    point exactly in the middle between the original and the new
    position of the point.

    Now, I have to prove whether or whether not it is possible to
    reposition the points, in order to get the following coordinates:
    1.(0;0)
    2.(1;1)
    3.(2;-1)
    4.(3;0)

    I've tried this little game quite intensively and I'm sure it is impossible but I still can't prove it.

    If I did not express myself clearly enough, let me give you an example of a possible move: You can move stone (0;0) to position (2;2) as stone (1;1) is exactly in the middle.
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  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Already answred here.

    RonL
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