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 line are vertical lines). Corresponding sides of these triangles are in the same ratio, so: If point "S" has coordinates ("x","m") then |"PS"| = |"y" - "m"| and the distance from "P" to the line is: Since "S" is on the line, we can find the value of m, and finally obtain: A variation of this proof is to place V at P and compute the area of the triangle ∆"UVT" two ways to obtain that formula_17 where D is the altitude of ∆"UVT" drawn to the hypoteneuse of ∆"UVT" from "P". The distance formula can then used to express formula_18,