# Glide reflection

In geometry, a**glide reflection**is a type of isometry of the Euclidean plane.

Within the isometry group of the plane, the product of a rotation and a translation can always be expressed as a single rotation (or translation). On the other hand the product of a reflection and a translation is usually not a reflection, but can produce a transformation with no everyday name: a **glide reflection**.

For example, there is an isometry consisting of the reflection on the *x*-axis, followed by translation of one unit parallel to it. In co-ordinates, it takes

- (
*x*,*y*) to (*x*+1,-*y*).

See also: congruence (geometry), similarity (mathematics), wallpaper group, frieze group.