Vectors are invariant under
translation. This means that they are unaffected or unchanged even if the
coordinates are translated. So while the coordinates of two points are changed
or moved during translation, the distance between the two points does not
change. The best way to picture this out is using real life scenario. For example,
you and I are at rest relative to each other but sitting on a plane at
different locations, then we will have a fixed distance. Now the plane flies
and its overall location is changed, similarly our individual coordinates also
change but the distance between us will remain the same.
