Translation (geometry)

In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure, shape or space the same distance in a single given direction, equivalent to adding a constant vector to every point or to shifting the origin of the coordinate system. Every translation in Euclidean space is an isometry, meaning it preserves the direction and length of line segments as well as the size of angles, and unlike a rotation it never turns the figure it acts on. Elevators, escalators and slides are cited as everyday practical examples of translation, and in translational symmetry a figure or motif slides along a line and repeats periodically while remaining otherwise unchanged, as in the repeating pattern of a frieze.