Supposed there's $(a,b)$ point and going to be reflected and find the mapping. The baseline formula will I use is $\begin{pmatrix} x' \\ y' \end{pmatrix}=M_{R} \begin{pmatrix} x \\ y \end{pmatrix}$. $M_{R}$ is reflection matrix.
I'd like to know reflection matrix about
- $y=\tan \theta \cdot x$. Quick search in Google gives $(A) \begin{pmatrix} \cos{2\theta} & \sin{2\theta} \\ \sin{2\theta} & -\cos{2\theta} \end{pmatrix}$. I inserted $(A)$ because I'm worry the right-side matrix needs to be multiplied with $m$ gradient or other stuff presents here. $(A)$ is not matrix.
- $y=\tan \theta \cdot x$ when the reference point is not the origin.
- $y=-\tan \theta \cdot x$. Should I just give negative sign to $\begin{pmatrix} \cos{2\theta} & \sin{2\theta} \\ \sin{2\theta} & -\cos{2\theta} \end{pmatrix}$?
- $y=-\tan \theta \cdot x$ when the reference point is not the origin (not $(0,0)$).
- $y=mx$ when the reference point is not the origin. I already have $y=mx$ when the reference point is $(0,0)$.
- $y=mx+c$.
- $y=mx+c$ when the reference point is not the origin. The baseline formula must be needs $+\begin{pmatrix} 0 \\ c \end{pmatrix}$ but I'm not sure.
Detail help is appreciated! Thanks.