A symmetry with respect to a line is determined by fixing the axis of symmetry. If $\vec v$ is a vector of the plane and $\vec v'$ is its image due to symmetry, their ends are equidistant from the axis.Furthermore, the vector $\vec v'-\vec v$ is perpendicular to the axis.

The fixed vectors of symmetry are those that lie on the axis.

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

In the drawing 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.