There are N points on a plane. Is it feasible to reproduce their relative location having only the list of distances. Assuming that translation, rotation and mirror are allowed in the result. The list contains only distances between every pair of points, but not which points these are.

For a simple triangle like A=(0,0) B=(1,0) C=(1,1) the distance are:
|AB| = 1
|AC| = sqrt(2)
|BC| = 1

The list would be: 1, 1, sqrt(2).