The correspondence in size, form, and arrangement of parts of opposite sides of a plane, line or point.

A type of symmetry.  Translating an object means moving it without rotating or reflecting it. 

Symmetry that takes place on a flat plane.  Plane symmetry involves moving all points around the plane so that their positions are relative to each other and remain the same, although their absolute positions may change.

The reflection of a figure in the plane about a line moves its reflected image to where it would appear if you viewed it using a mirror placed on the line.  Another way to make a reflection is to fold a piece of paper and trace the figure onto the other side of the fold.