Motion, translation and symmetry about a line

Drop a perpendicular from M to the line a and call its foot O. The point M₁ on the perpendicular with MO = M₁O is symmetric to M about a. Sending every point of the plane to its symmetric point is called symmetry about a line (reflection); it is a motion, so distances are preserved, but the orientation of angles reverses. In coordinates, A(x; y) goes to (x; −y) about the Ox axis and to (−x; y) about the Oy axis. If a figure maps to itself about a line, that line is its axis of symmetry. For example a rectangle has 2 axes, a square 4, a rhombus 2, an isosceles triangle 1 and an equilateral triangle 3.