What is glide reflection in geometry?

Glide reflection is a type of transformation in geometry which is a combination of reflection and translation. In a glide reflection, an object is first reflected over a particular line and then translated parallel to that line. This transformation changes the position of the object but does not change its shape or size.

The line of reflection and the distance of the translation are both important parts of a glide reflection. For example, if a triangle is reflected over a vertical line and then translated horizontally by a certain distance, it will produce a different image from the same triangle being reflected over a different vertical line and translated by a different distance.

Glide reflections are used in various applications in geometry, such as in crystallography, where they are used to describe the symmetry of crystals. They are also used in the study of fractals and other geometric patterns.