Intuitive Notion of Point Symmetry
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Point symmetry exists when a figure is built around a single point called the center of the figure.  For every point in the figure, there is another point found directly opposite it on the other side of the center.

Study the diagrams below:

This figure shows two points and their reflections through a line.  This is line symmetry.

This figure shows two points and their reflections through a point.  This is point symmetry.

 

In a point symmetry, the center point is a midpoint
to every segment formed by joining a point to its image. 

 

A simple test to determine whether a figure has point symmetry is to turn it upside-down and see  if it looks the same.  A figure that has point symmetry is unchanged in appearance by a 180 degree rotation.