The Product of a Half-Turn and a Line Reflection is a Glide Reflection

(Except that it is a line reflection when the center of the half-turn is on the mirror line.)

This interactive figure portrays a point P and its image Q by a glide reflection that translates by vector AB and then reflects across line AB.

The figure shows that Q can also be constructed by first rotating P with center A by 180 degrees (a halfturn) and then by reflecting across the line m.

For more details about the figure and the theorem it illustrates, go to this link.

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Glide Reflection Two Ways

James King, 11/18/2005

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