A transformation that slides every point of a figure or space by the same amount in a given direction is defined by a specific quantity. This quantity possesses both magnitude and direction, effectively shifting the object without rotation or resizing. Imagine a triangle moved three units to the right and two units upwards; this movement is fully described by the component that specifies the horizontal shift and another specifying the vertical shift.
Such a directed quantity is fundamental in numerous fields. In computer graphics, it allows objects to be repositioned on a screen. In physics, it can represent the displacement of an object from one location to another. Its simplicity and ability to precisely define spatial shifts make it an indispensable tool in various mathematical and scientific disciplines. Early geometric investigations implicitly used similar concepts, but the formalization into a specific mathematical entity provided a robust framework for analyzing and manipulating spatial relationships.