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Consider two sets in the Euclidean plane, each consisting of 4 points.

First set:  A(0, 0),  B(3, 4),  C(12, 4),  E(4, -1)

Second set:  F(0, -8),  G(12, -4),  H(9, -8),  K(4, -9)

It is easy to check that the set of all pairwise distances between the points of each of the given sets (6 numbers for each set ) are the same. At the same time it is obvious that there is no any...

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...