(adsbygoogle = window.adsbygoogle || []).push({}); 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.

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# Homework Help: Linear transformation across a line

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