Glide vs (Reflection and Translation)

Author:
Mark Sawula
Topic:
Geometric Transformations
A glide is an isometry in which an object is
  • reflected across a mirror line, and then
  • translated by a vector parallel to the line
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.
  1. Is any combination of reflection and translation equivalent to a glide? 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?
  2. What is the relationship between the red vector and the purple mirror line? Can you see how the position of the red vector depends on both the position of the purple line and the cyan vector?

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