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Using linear transformation reflection to find rotation
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?
[itex]\frac{1}{1+m^2}\begin{pmatrix}
1-m^2 & 2m\\
2m & m^2-1
\end{pmatrix}[/itex]
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.
Homework Statement
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?
Homework Equations
[itex]\frac{1}{1+m^2}\begin{pmatrix}
1-m^2 & 2m\\
2m & m^2-1
\end{pmatrix}[/itex]
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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