Math 444 Quiz 5

  1. (20 points)

    2. (a) The segment AB is perpendicular to line m. If s is reflection in line m and t is translation by vector AB, state clearly what isometry is the composition

    a = st.

    Your statement should be completely unambiguous about the location of the defining objects (such as centers, vectors mirror lines) of a.

     

     

     

     

     

     

    (b) Prove your statement in (a) using the definitions and theorems at your disposal (not including the results about composing translations and reflections or glide reflections of course).

     

  2. In the figure below, mark all the centers of rotation (fat dots for 180 degrees, squares for 90 degrees, etc.), mark the mirror lines with double lines and the nontrivial glide reflections with dashed lines. Also indicate the basic translations t and t' and shade in one of the parallelograms defined by these translations.

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