Translation (geometry)

A translation is a transformation that shifts every point of a figure by the same distance in the same direction. It's one of the most fundamental operations in Computer graphics, mathematics, and physics—a pure sliding motion with no rotation, scaling, or distortion.

Translations preserve all distances and angles, making them isometries: the translated shape is congruent to the original. In coordinate systems, a translation moves point (x, y) to (x + a, y + b) for constants a and b. The concept scales to any dimension, from moving a point along a Curve to shifting volumes through 3D space.

Translations appear everywhere: in Group theory, they form a fundamental group of symmetries; in Computer graphics, they position objects on screen; in physics, they describe motion without rotation. Archimedes and other ancient mathematicians implicitly used translation when reasoning about volumes and areas.

The elegance of translation lies in its simplicity—it's the most basic way to move something without changing its shape. Combined with rotations and reflections, translations comprise the complete set of rigid motions in space, forming the foundation of geometric symmetry.

Related

Transformation (geometry), Group theory, Computer graphics, Tangent line, Mirror