I want to express the isometry $R_{(4,4), \frac\pi2}F_{x+3y=6}$ (where $R$ is a rotation about $(4,4)$ by $\frac\pi2$) as a glide reflection.
Here's my attempt:
$R_{(4,4), \frac\pi2}F_{x+3y=6}((x,y))=(T_{(4,4)}+R_{\frac\pi2})(F_{x+3y=6}((x,y))-(4,4))\\=T_{(4,4)}F_{x+3y=6}((x,y))-T_{(4,4)}(4,4)+R_{\frac\pi2}F_{x+3y=6}((x,y))-R_{\frac\pi2}((4,4))\\=G_{(4,4),x+3y=6}((x,y))-(4,4)+R_{\frac\pi2}F_{x+3y=6}((x,y))-R_{\frac\pi2}((4,4)).$
Now, I totally lack an idea about what to do next. Would appreciate some help.