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Point Symmetry is when every part has a matching part the same distance from the central point but in the opposite direction. Thus a symmetry can be thought of as an immunity to change. When every part of a figure has a matching part in the opposite direction from the central point it is said to have point symmetry.
A central symmetry centered at point O is a movement of the plane where every point P of the plane has to map to another point P being O the average point of the segment of endpoints P and P.
In geometry an object has symmetry if there is an operation or transformation such as translation scaling rotation or reflection that maps the figureobject onto itself ie the object has an invariance under the transform. A figure has point symmetry if it can be reflected across a point back on to itself. It is also the same as Rotational Symmetry of Order 2. Any line splitting a shape into two parts such that the two parts are the same is called a line of symmetry.