Parallel shift

From Wikipedia, the free encyclopedia

Parallel shift is a shift of all the points in one and the same direction on one and the same distance.

If $M$ is the starting point and $M'$ is the same point but shifted, then the vector $\overrightarrow{MM'}$ will be the same for all the other points that are shifted.

On a plane the parallel shift can be presented analitically in the Cartesian coordinate system as $(x, y)$ vector using $(x,y)\mapsto(x+a,y+b),$ , where the $\overrightarrow{MM'}=(a,b)$ .