1. Reflection: The figure is reflected across a line (the line of reflection).
2. Translation: The reflected figure is then translated along a line parallel to the line of reflection.
In other words, a glide reflection is like sliding a figure across a surface and then flipping it over.
Here's a more formal definition:
Glide Reflection: A transformation that is a composition of a reflection across a line followed by a translation in the direction of that line.
Key Features:
* Direction: The translation is always parallel to the line of reflection.
* Distance: The distance of the translation is the same for all points of the figure.
* Isometry: Glide reflections are isometries, meaning they preserve distances and angles.
Examples:
* Imagine you're sliding a book across a table and then flipping it over so the cover is facing down. This is a glide reflection.
* A pattern on a wallpaper that repeats in a diagonal direction often utilizes glide reflections.
Notation:
Glide reflections are often denoted by "g" followed by the line of reflection and the direction and distance of the translation. For example, "g_l(d)" represents a glide reflection across line l, with a translation of distance d along a line parallel to l.