An **isometry** is a function that maps the
plane to itself which
preserves distances. If *M* is an isometry, we will denote the point to which *M* moves a point *A* by *M*(*A*). When we say
that an isometry preserves distances we mean that

An isometry *M* is said to be **invertible** if there is another
isometry *M*^{-1} such that

for every point A in the plane.

A **translation** is a map of the form

*T*((*x* , *y*) = (*x* - *x*_{0} , *y* - *y*_{0})

for some point (*x*_{0},* y*_{0}) in the plane.

Given a line, to
**reflect** a point across
the line, move the point
perpendicularly to
the line and then move it the
same distance beyond the
line. Such a map is called a
**reflection**.