Let $\tau_{w}$ be any translation and let $\ell = P + [w^{\perp}]$ be any line having $w$ as normal vector. Show that if $m = P - \dfrac{1}{2} w + [w^{\perp}]$ and $m^{\prime} = P + \dfrac{1}{2} w + [w^{\perp}]$, then
$$\Omega_{\ell} \Omega_{m} = \Omega_{m^{\prime}} \Omega_{\ell} = \tau_{w}$$
I need some light on this. Thanks. :]