Translation (geometry) of the object. The translation vector formula_8 common to all points of the object describes a particular type of displacement of the object, usually called a "linear" displacement to distinguish it from displacements involving rotation, called "angular" displacements. When considering spacetime, a change of time coordinate is considered to be a translation. For example, the Galilean group and the Poincaré group include translations with respect to time. 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
Distance from a point to a plane the point on a plane formula_33 closest to an arbitrary point formula_34 is formula_2 given by where and the distance from the point to the plane is 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