In the context of mathematics, "translation" typically refers to a specific type of transformation that moves points in a geometric figure or coordinate system without changing their shape, size, or orientation.
For example, in the coordinate plane, a translation can be defined by specifying a vector (an arrow with direction and length) that indicates how far and in which direction to move each point of a shape. If you have a point at coordinates \((x, y)\) and you apply a translation defined by the vector \((a, b)\), the new coordinates of the point after translation will be \((x + a, y + b)\).
Translations can be expressed in various areas of mathematics, such as geometry, algebra, and vector analysis, and are a fundamental concept in the study of transformations.