In the figure below, the black R was reflected across the purple line. The image of that reflection (the purple 'ya') was then reflected across the cyan line. [list=1] [*][i]Can a reflection of a reflection be a translation?[/i] Try to move the purple and cyan lines so that the cyan R is just a translation of the black R. Then adjust the red vector so that the red R coincides with the cyan one. You have just shown that a reflection of a reflection can be a translation. [*][i]Can a reflection of a reflection be a 'do nothing'? [/i]Adjust the purple and cyan lines so that the cyan R coincides with the black one. [/list]