Let c be a fixed point in the plane. By the reflection (or half-turn)  in  point c we mean the transformation of S onto itself which carries each point P of the plane into the point Q of the plane such that c is the midpoint of PQ. Point c is called the center of the reflection.

Let c be a fixed line in the plane. By the reflection  about line c we mean the transformation of S onto itself which carries each point P of the plane into the point Q of the plane such that c goes through the midpoint of PQ and is perpendicular to PQ.

For a detailed description of the object created Q, use the routine detail (i.e., detail(Q))

The command with(geometry,reflection) allows the use of the abbreviated form of this command.

assume that the names of the horizontal and vertical axes are _x and _y, respectively