Point Reflection

The point reflection of a point \(M\) in a point \(O\) is the point \(M'\) such that \(O\) is the midpoint of the segment \(\Segment{MM'}\). In other words, \(OM = OM'\) and the three points \(M\), \(O\) and \(M'\) lie on the same straight line.

The point reflection of an object in a point \(O\) is obtained by taking the point reflection in \(O\) of all its points. The image has the same size and shape as the object, but it is turned \(180^\circ\) around \(O\).

A point is a center of symmetry of an object if the point reflection of the object in this point coincides exactly with the object. In other words, the object does not change when it is reflected in this point.