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Math Help - Prove that P(n) o P(m) = T (ab)

  1. #1
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    Prove that P(n) o P(m) = T (ab)

    I need help to prove the following proposition.

    Proposition: Let m and n be two parallel straight lines. Let AB be a line segment that first intersects m and then n, that is perpendicular to both m and n, and whose length is twice the distance between m and n. Then Pn o Pm = T (AB)

    Note: P is reflection and T is translation

    Thank you!
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  2. #2
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    Since the problem can be translated and rotated at will, choose m and n so that the question is most easily answered. I choose m as the x=0 line, and n as the x=a line. Let your test point A be (x,0). Then P(m) on A gives (-x,0), and P(n) on (-x,0) gives (x+2a,0). Clearly that's T(ab).
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  3. #3
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    Quote Originally Posted by qmech View Post
    Since the problem can be translated and rotated at will, choose m and n so that the question is most easily answered. I choose m as the x=0 line, and n as the x=a line. Let your test point A be (x,0). Then P(m) on A gives (-x,0), and P(n) on (-x,0) gives (x+2a,0). Clearly that's T(ab).

    I went to someone for this problem, and that person showed me a different way of proof. Your is good, but it is still unclear why it is T(ab) for the T(ab) is not defined. Thank you.
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