$\text{For a given line L, let}{\mathrm{\Omega}}_{l}(x)\text{be the relectoin of point X with respect to line L.}\phantom{\rule{0ex}{0ex}}{\mathrm{\Omega}}_{l}(x)=X\text{if and only if X is in L.}\phantom{\rule{0ex}{0ex}}\text{This is what I did but I don't think you can do what I did.}\phantom{\rule{0ex}{0ex}}{\mathrm{\Omega}}_{l}(x)=X\phantom{\rule{0ex}{0ex}}d({\mathrm{\Omega}}_{l}(x),X)=0\phantom{\rule{0ex}{0ex}}d(X,{\mathrm{\Omega}}_{l}(x))=X={\mathrm{\Omega}}_{l}(x)$