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 line formula_39 perpendicular to the line. The distance from the point to the line is then just the norm of that vector. This more general formula is not restricted to two dimensions. If the vector space is orthonormal and if the line ("l" ) goes through point A and has a direction vector formula_45, the distance between point P and line ("l") is where formula_47 is the cross product of the vectors formula_48 and formula_45 and where formula_50 is the vector norm of formula_45. Note that cross products only exist in dimensions 3 and 7. Distance from a point to a