A geometric transformation shifts every point of a figure or space by the same distance in a given direction. This operation is fully defined by a mathematical object that specifies both the magnitude and direction of the shift. For instance, consider a triangle on a coordinate plane. Applying this operation moves the triangle without rotating or resizing it; the resulting triangle is congruent to the original, merely existing in a different location. The shift is consistent across all vertices of the triangle.
The significance of this operation lies in its preservation of shape and size, making it fundamental in various fields. Historically, it has been essential in cartography for map projections and in physics for describing the motion of objects. Furthermore, it simplifies complex geometric problems by allowing figures to be repositioned for easier analysis or calculation. In computer graphics, it is a building block for animation and object manipulation within a virtual environment.