A symmetry with respect to a line is determined by fixing the axis of symmetry. If P is a point in the plane and   P' is its image throught the symmetry, both points are equidistant from the axis of symmetry. Furthermore, the vector that joins P and P' is perpendicular to the axis.

The fixed points of symmetry are those of the axis.

Symmetries preserve angles and distances. But do they keep their orientation? 

In the figure we see what is the image of a triangle by a symmetry with respect to a line. You can check how the symmetries behave in the plane, modifying the axis of symmetry and the vertices of the triangle.