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Unformatted text preview: ρ D, Φ such that τ A,B = ρ D, Φ ρ C,θ ? 7. State if the following are True or False . If true give a short proof. Otherwise give a counterexample (whenever it is possible to do so). (a) σ P σ ‘ σ P σ ‘ σ P σ ‘ σ P is a reﬂection in a line parallel to line ‘ . (b) ρ B, Φ ρ A,-Φ is the translation that takes A to ρ B, Φ ( A ) . (c) Every isometry is a product of two involutions. (d) If n > 2 then D n is generated by two reﬂections. 1 (e) A group of isometries of order 143 must be a cyclic group C 143 . 8. What are the equations for ρ O,π/ 3 and ρ (1 ,-2) ,π/ 3 ? 9. What is the test for the symmetry with respect to the line ‘ with an equation y = 2 x-1 ? 10. Let ‘ be the line with an equation of the form y = mx + b and P = ( a,ma + k ) be a point . If f = τ O,P σ ‘ ﬁnd equations for the glide reﬂection f by using question 4. 2...
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