Translation (geometry) Translation (geometry) In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure or a space by the same distance in a given direction. In Euclidean geometry a transformation is a one-to-one correspondence between two sets of points or a mapping from one plane to another. A translation can be described as a rigid motion: the other rigid motions are rotations, reflections and glide reflections. A translation can also be interpreted as the addition of a constant vector to every point, or as shifting the origin of the coordinate system. A translation operator is an
Distance from a point to a plane Distance from a point to a plane In Euclidean space, the point on a plane formula_1 that is closest to the origin has the Cartesian coordinates formula_2, where The distance between the origin and point formula_2 is formula_5. If what is desired is the distance from a point not at the origin to the nearest point on a plane, this can be found by a change of variables that moves the origin to coincide with the given point. Suppose we wish to find the nearest point on a plane to the point (formula_6), where the plane is given by formula_7.