Reflection in an axis

Let a line l and a point A be given in the plane. Draw the perpendicular AB from A to l and extend it beyond B by a segment BA1 equal to AB; then A1 is the point symmetric to A about l, and l is the axis of symmetry. A point on the axis is regarded as symmetric to itself. If every point of a figure F1 is symmetric about l to a point of F, the figures F and F1 are symmetric about l, and they are congruent. Theorem: under reflection in an axis the distances between points of a figure are preserved. In coordinates: about the Ox axis the point (x; y) goes to (x; −y), and about the Oy axis it goes to (−x; y).