translation

Sliding every point of a shape by the same fixed amount in the same direction.

A translation shifts every point $p$ by a fixed vector $t$ , written $T(p) = p + t$ . It moves a shape's position without changing its size, orientation, or angles -- and it is the one ordinary 2D transform that a $2\times2$ matrix alone can never represent, since it moves the origin.

Examples

Sliding a photo 3 pixels right and 2 pixels down is a translation: every one of its pixels moves by the same $(3,-2)$ shift.