Exploring Two Reflections with Parallel Lines
While the letter F is double reflected about two parallel lines, the lesson being shown applies to all similar reflections. Check each box separately/together to learn how the coordinates relate the mirror (the y-axis here for ease of learning. Drag point L to see how the transformations change, but what property stays the same?
http://www.maa.org/sites/default/files/images/upload_library/47/Crowe/GeoGebra_Activity_5.html by Cheryll E. Crowe, Eastern Kentucky University