I have the following transformation:
$f(x,y)=(-\frac{3}{5}x+\frac{4}{5}y -\frac{4}{5},\frac{4}{5}x+\frac{3}{5}y+\frac{2}{5})$ which is the reflection on the the straight line defined by $y=2x+1$
I'm asked the following: Give a pair of lines $m$ and $l$ for which the isometry $g=(R_l \circ f \circ R_m)^2$ satisfies $g(0,0)=(2,4)$ where $R_l$ denotes the reflection on the line $l$.
I have concluded that $R_l \circ f \circ R_m$ must be an inverse isometry, but not a reflection, otherwise $g(0,0)=(0,0)$, I guess it must be a glide reflection, but I don't know a smart aproach to find the straight lines $m$ and $l$.