The plane we are dealing with is $\mathbb{R}^2$.
Notations:
- $H_a = R(a,\pi)$ which means a rotation about the point $a$ for $\pi$.
- $G(l,a)=R_lT_a$ which means a glide that is a composition of a reflection about the line $l$ and a translation with a vector $a$.
I would share a solution for this problem which I'm having trouble understanding.
Given a line $l$ and $a$ (the solution didn't specify what is $a$, but this should be a vector), choose a point $b$ on $l$.
Then, we can check that $H_bG(l,a)=R_{l'}$, where $l'$ is a perpendicular line to $l$ and $l\cap l'$ is given by $b-\frac{a}{2}$.
Then, $G(l,a)=H_bR_{l'}$.
I'm not really sure how the $l'$ is defined here.
I was assuming that $b-\frac{a}{2}$ gives some point, then we draw a line $l'$ from this point perpendicularly to $l$. However, this didn't really work.