# Application of Linear Transformation: Robot (선형변환의 응용: 마징가Z)

Reflection in a given line
The transformation matrix $T$ for a reflection in given a line $ax+by+c=0$ is given by
$T=\large { \begin{bmatrix} \frac{-(a^2 - b^2)}{a^2+b^2} & \frac{-2ab}{a^2 + b^2} & \frac{-2ac}{a^2 + b^2} \\ \frac{-2ab}{a^2 + b^2} & \frac{a^2 - b^2}{a^2+b^2} & \frac{-2bc}{a^2 + b^2}\\ 0 & 0 & 1 \end{bmatrix}}$,     where $b \neq 0$.