Abstract
This paper presents theorems about the form of probability distributions of Euclidean distances between ordered sets of points in the plane for random transformations of their subsets. Four options are considered for the change: a random rotation as a whole, a random reflection as a whole, simultaneous independent random rotations of two ordered disjoint subsets that make up the original ordered set, and simultaneous independent random reflection of two ordered disjoint subsets that make up the original ordered set. The theorems contain expressions to calculate the probability density function to calculate the initial moments.
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