Letland m be lines such that om (l) = l. Prove that either l = = m 01 l I m.

Let m be a line. The reflection in line m is the transformation ${\sigma }_m:R^2\to R^2$ with the following properties:
1. If P is a point on m, then,${\sigma }_m(P)=P$ i.e., ${\sigma }_m$ fixes line m pointwise.
2. If P is a point off m and $P^{\prime }={\sigma }_m(P),$ then m is the perpendicularbisector of PP'.
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