Refleksi

Konsep Dasar

 

REFLEKSI MATRIKS REFLEKSI HASIL REFLEKSI
Sumbu X \(\begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}\) \(\begin{pmatrix} x' \\ y' \end{pmatrix} = \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix}\)
Sumbu Y \(\begin{pmatrix} -1 & 0 \\ 0 & 1 \end{pmatrix}\) \(\begin{pmatrix} x' \\ y' \end{pmatrix} = \begin{pmatrix} -1 & 0 \\ 0 & 1 \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix}\)
Garis \(y = x\) \(\begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}\) \(\begin{pmatrix} x' \\ y' \end{pmatrix} = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix}\)
Garis \(y = -x\) \(\begin{pmatrix} 0 & -1 \\ -1 & 0 \end{pmatrix}\) \(\begin{pmatrix} x' \\ y' \end{pmatrix} = \begin{pmatrix} 0 & -1 \\ -1 & 0 \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix}\)
Garis \(x = a\) \(\begin{pmatrix} -1 & 0 \\ 0 & 1 \end{pmatrix}\) \(\begin{pmatrix} x' - a \\ y' \end{pmatrix} = \begin{pmatrix} -1 & 0 \\ 0 & 1 \end{pmatrix} \begin{pmatrix} x - a \\ y \end{pmatrix}\)
Garis \(y = b\) \(\begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}\) \(\begin{pmatrix} x' \\ y' - b \end{pmatrix} = \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix} \begin{pmatrix} x \\ y - b \end{pmatrix}\)
Titik \((a,b)\) \(\begin{pmatrix} -1 & 0 \\ 0 & -1 \end{pmatrix}\) \(\begin{pmatrix} x' - a \\ y' - b \end{pmatrix} = \begin{pmatrix} -1 & 0 \\ 0 & -1 \end{pmatrix} \begin{pmatrix} x - a \\ y - b \end{pmatrix}\)
Garis \(y = mx + c\)

\(m = \tan \theta\)

\(\begin{pmatrix} \cos 2 \theta & \sin 2 \theta \\ \sin 2 \theta & -\cos 2 \theta \end{pmatrix}\) \(\begin{pmatrix} x' \\ y' \end{pmatrix} = \begin{pmatrix} \cos 2 \theta & \sin 2 \theta \\ \sin 2 \theta & -\cos 2 \theta \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} + \dfrac cm \begin{pmatrix} -2 \sin^2 \theta \\ \sin 2 \theta \end{pmatrix}\)
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