Let us say we require to find the reflection of $(x_{1},y_{1})$ about the line $y=x\tan\theta$. So it can be done by using the following formula easily.
$$\frac{h-x_{1}}{\tan\theta}=\frac{k-y_{1}}{-1}=\frac{-2(x_{1}\tan\theta-y_{1})}{1+\tan^2\theta}$$
We also have, $k=h\tan(\theta-\alpha)$ and $y_{1}=x_{1}\tan(\theta+\alpha)$. I wish to prove this result geometrically, is there a way to do so. Any hints are appreciated. Thanks.