# 466-HW-4 - (d) If A and B are two distinct points, | PA | =...

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Math 466 - Homework Set 4 (10.11.2011) 1. Let A = (0 , 0) , B = (5 , 0) , C = (0 , 10) , D = (4 , 2) , E = (1 , - 2) and F = (12 , - 4) . Assume that 4 ABC = 4 DEF . Find equations of lines such that the product of reﬂections in these lines maps 4 ABC to 4 DEF . 2. Let ‘, m and n be the lines with equations x = 2 , y = 3 and y = 5 , respectively. Find the equations for σ m σ and σ n σ m . 3. 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) The images of a triangle under two distinct isometries cannot be identical. (b) A product of four reﬂections is an isometry. (c) The set of all rotations generates an abelian group.
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Unformatted text preview: (d) If A and B are two distinct points, | PA | = | PB | and | QA | = | QB | then P = Q . (e) An isometry that ﬁxes a point is an involution. (f) If an isometry f ﬁxes points A, B and C then f = ι . (g) ρ-1 C, θ = ρ C,-θ = σ C for any point C . (h) If a directed angle from a line ‘ to a line m is 4 π/ 3 radians then σ m σ ‘ is a rotation through 2 π/ 3 radians. (i) σ m σ ‘ = τ 2 L, M = σ M σ L if point L is on line ‘ and point M is on line m . 1...
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## This note was uploaded on 12/26/2011 for the course MATH 466 taught by Professor Ytalu during the Spring '11 term at Middle East Technical University.

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