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.