Question: Isometry of the sets in Euclidean plane

February 05 2013 Kitonum 3420
Maple

2

Here is , seemingly simple task:
In the Euclidean plane are given two sets, each with 4 points. It is known that all possible pairwise distances between the points of the first set coincide with all possible pairwise distances between the points of the second set, ie we obtain two sets of numbers, in each of which six numbers. Of course, the numbers in each numeric set can be repeated (such sets are called multisets).  Can we say that there is an isometry of the plane taking the first set of points on the second?

This question arose in my communication with the writing algorithm checking of two sets of points on the plane to be isometric. I know the answer, but do not tell that everyone can enjoy the process of the solution. Perhaps this question has been discussed elsewhere. Who met - please provide a link, but not immediately, but after a while.

It is also interesting can this question be solved with Maple?

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