On distribution of euclidean distances between ordered set of plane points at random rotation and reflection

In the paper the dependence of location of the ordered finite set of points in a plane from the action of random rotations and reflections has been researched. The location changing has been estimated by Euclidean distance between the original set of points and the set of points obtained after the transformation. We consider four options of transformation of an ordered set of points: a random rotation as a whole, random reflection as a whole, simultaneous independent random rotations of two ordered disjoint subsets that make up the initial ordered set, simultaneous random reflections of two ordered disjoint subsets that make up the original ordered set. We have derived expressions for the probability density functions and formulas for calculating the ordinary moments for all four variants.