Rigid Motion

A rigid motion, or isometry, is a transformation that preserves the distance between any two points on the preimage. AB=A'B' The following diagram displays two logos. The logo with the points A and B is the preimage, and the logo with the points A' and B' is the image. The image is the result of a rigid motion because the distances between all points are preserved.

Rigid motions are also called congruence transformations. That is because the preimage and its image under a rigid motion are congruent figures. Some examples of rigid motions are translations, reflections, and rotations.

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A Composition of Rigid Motions

A composition of a translation, a rotation, and a reflection is also a rigid motion because it preserves the distance between any two points on the preimage.

Notice that this type of transformation also preserves the angle measures of the figure. However, its position and orientation can sometimes be affected.