Glide vs (Reflection and Translation)

A [i]glide[/i] is an isometry in which an object is [list] [*]reflected across a mirror line, and then [*]translated by a vector parallel to the line [/list] In this exploration, the black R is reflected across the purple mirror line producing a purple 'ya'. The 'ya' is then translated by the cyan vector which is not necessarily parallel to the mirror. Meanwhile a glide of the black R is controlled by a tricky representation of the red vector. The red vector also contains a red line segment. The black R is reflected across that red segment and then translated by the vector. [list=1] [*][i]Is any combination of reflection and translation equivalent to a glide?[/i] Move the red vector so that the red 'ya' coincides with the cyan 'ya'. Are there any versions of the cyan vector for which this can't be done? [*][i]What is the relationship between the red vector and the purple mirror line?[/i] Can you see how the position of the red vector depends on both the position of the purple line and the cyan vector? [/list]