Translation in geometry is a type of transformation that moves every point of a figure, shape, or space by the same distance in a given direction). It is one of the four types of transformations in geometry, which also include rotations, reflections, and dilations. A translation can be interpreted as the addition of a constant vector to every point, or as shifting the origin of the coordinate system). In a Euclidean space, any translation is an isometry, meaning that it preserves distances between points).

To perform a translation, every point of the shape must move without rotating, resizing, or anything else, just moving. The translation can be described by a vector, which represents the distance and direction of the movement. For example, to say that a shape gets moved 30 units in the "X" direction and 40 units in the "Y" direction, we can write: (x,y) → (x+30,y+40) .

Translations can be horizontal or vertical, depending on the direction of the movement. A horizontal translation moves a shape left or right, while a vertical translation moves a shape up or down). When a shape has been transformed, the original shape is called the preimage, and the translated shape is called the image. The size and shape of the image remain unaffected after the translation.

In summary, translation in geometry is a transformation that moves every point of a figure, shape, or space by the same distance in a given direction. It is an isometry that preserves distances between points. Translations can be horizontal or vertical, and they do not change the size or shape of the original shape.