A geometric transformation that shifts every point of a figure or space by the same distance in a given direction is defined by a vector. This operation maintains the size and shape of the original object, only changing its position. For instance, if each vertex of a polygon is moved three units to the right and two units up, the resulting polygon is a congruent image of the original, simply relocated on the plane.
This method offers a fundamental operation in various fields, including computer graphics, physics, and engineering. It simplifies complex calculations involving motion or spatial relationships. Historically, it provided a basis for understanding more complex transformations and laid the groundwork for advanced geometrical concepts.