What is the definition of a translation in mathematical terms?

A translation in mathematical terms refers to a specific type of transformation that involves moving a figure from one location to another without altering its shape, size, or orientation. This movement is defined by a vector, which indicates both the direction and distance of the slide. For example, if a point on a graph is translated by the vector (3, 2), it will move 3 units to the right and 2 units up from its original position, effectively "sliding" to a new location.

In contrast, the other definitions provided focus on different mathematical transformations. A change of direction or angle pertains more to rotation, changing the position of a shape around a point. A change of size or shape relates to dilation or scaling, which modifies the dimensions of a figure. Lastly, a flip over a line of symmetry describes a reflection, where a figure is mirrored across a specified line. Each of these transformations serves different functions in geometry, setting them apart from the concept of translation.