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Homework 2 - due Monday
All the questions from Tuesday.
Question 9.1. Sketch the fixed point of rt rs where rs = rn rm rl and rt = ra rb rc , and all the
lines are as shown in the figure below.
Question 9.2. Given a figure consisting of two points P and Q, sketch a construction of
the fixed point of tP,Q rP,45 .
Question 9.3. Given a figure consisting of three points A, B and C, sketch a construction
of the fixed point of tB,C rA,120 .
Question 9.4. What are the equations for rn rm if line m has equation y = −2x + 3 and
line n has equation y = −2x + 8?
Question 9.5. If rn rm (x, y) = (x + 6, y − 3), find equations for lines m and n.
Question 9.6. Classify all isometries of the plane. This basically means that you should
write up in some coherent way our work from the past several days. All of the things you
decide to include should be accompanied by the proofs of the statements.
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