Exercise 1.5.7

Question

Find the matrix of the reflection through the line $y=-2x/3$. Perform all the multiplications.

Jing Huang · Accepted Answer

extbf{Solution} \emph{(Similar to \href{./exercise_1-5-4}{Problem 5.4} though not exactly the same.)}
\begin{equation*}
  \begin{split}
    T &= 
    R(\alpha)RefR(-\alpha) \
    &=
    R(\alpha)
    \begin{bmatrix}
    1 & 0 \
    0 & -1 \
    \end{bmatrix}
    R(-\alpha).
  \end{split}
\end{equation*}
$\alpha = 	an^{-1}(-\frac{2}{3})$, so we can get the matrix is 
\begin{equation*}
    T = 
    \begin{bmatrix}
    \frac{5}{13} & -\frac{12}{13} \
    -\frac{12}{13} & -\frac{5}{13} \
    \end{bmatrix}.
\end{equation*}

Exercise 1.5.7

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Exercise 1.5.7

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