A translation or slide involves moving a figure in a specific
direction for a specific distance. Vectors are often used to
denote translation, because the vector communicates both a
distance (its length) and a direction (the way it is pointing).
The vector shows both the length and direction of the
translation. A glide reflection is a combination of two
transformations: a reflection over a line, followed by a
translation in the same direction as the line. Reflect over the
line shown; then translate parallel to that line. Only an
infinite strip can have translation symmetry or glide reflection
symmetry. For translation symmetry, you can slide the whole
strip some distance, and the pattern will land back on itself.
For glide reflection symmetry, you can reflect the pattern over
some line, then slide in the direction of that line, and it
looks unchanged. The patterns must go on forever in both
directions.