The Glide Reflection is an isometry because it is defined as the composition of two isometries: º Ml, where P and Q are points on line l or a vector parallel to line l. An issue, of course, is whether this composition is equivalent to some existing isometry -- a reflection, rotation, or translation.

Is glide reflection an isometry?

A glide-reflection is an isometry that is the product of a reflection and a translation in the direction of the axis of the reflection.

Why is a translation an isometry?

In a translation, ALL of the points move the same distance in the same direction. A translation is called a rigid transformation or isometry because the image is the same size and shape as the pre-image.