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Linear transformation across a line

  1. Nov 25, 2012 #1
    Using linear transformation reflection to find rotation

    1. The problem statement, all variables and given/known data
    Let [itex]T1[/itex] be the reflection about the line [itex]−4x−1y=0[/itex] and [itex]T2[/itex] be the reflection about the line [itex]4x−5y=0[/itex] in the euclidean plane.

    The standard matrix of [itex]T1 \circ T2[/itex] is what?

    Thus [itex]T1 \circ T2[/itex] is a counterclockwise rotation about the origin by an angle of how many radians?


    2. Relevant equations

    [itex]\frac{1}{1+m^2}\begin{pmatrix}
    1-m^2 & 2m\\
    2m & m^2-1
    \end{pmatrix}[/itex]


    3. The attempt at a solution

    I've used the relevant equation above and found that [itex]T1 \circ T2 = \begin{pmatrix}
    \frac{-455}{697} & \frac{-528}{697}\\
    \frac{-455}{697} & \frac{-455}{697}\end{pmatrix}[/itex] and had this verified, but I have no idea how to relate this into an amount of radians rotated.
     
    Last edited: Nov 25, 2012
  2. jcsd
  3. Nov 25, 2012 #2

    tiny-tim

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    Science Advisor
    Homework Helper

    hi 1up20x6! :smile:

    should be [itex]\begin{pmatrix}
    \cos & \sin\\
    -\sin & \cos\end{pmatrix}[/itex] :wink:
     
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