An axial symmetry is a transformation, therefore each point on the plane maps another point also of the plane, so that the axis would be the perpendicular bisector of the segment
. The axial symmetries are inverse isometries, because they preserve the distances between its points and its homologous, but its orientation is inverse. The axial symmetry not only appears between an object and its reflection, since many figures that can break in two sections by means of a line are symmetrical with regard to the line. These objects have one (or more) symmetry axes.
The axial symmetry happens when the points of a figure coincide with the points of another one, taking as a reference a line that is known by the name of axis of symmetry. In the axial symmetry we find the same phenomenon as in an image reflected in the mirror.