An isometry of the Euclidean plane is a distance-preserving transformation of the plane. That is, it is a map

such that for any points p and q in the plane,

where d(p, q) is the usual Euclidean distance between p and q.

Classification

It can be shown that there are four types of Euclidean plane isometries. (Note: the notations for the types of isometries listed below are not completely standardised.)

Reflections

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