A translation is a rigid transformation in which every point of a figure is moved along the same direction through the same distance.

For instance, when ∆ABC is transformed to ∆A′B′C′, AB and A′B′ are parallel to the x-axis, and AC and A′C′ are parallel to the y-axis. Moreover, ∆ABC and ∆A′B′C′ have the same orientation. i.e., the way they face is the same. This type of transformation is said to be a translation.

Definition

A transformation T is said to be a translation if every point P = (x, y) of a plane is moved the same distance in the direction of a given vector =(h,k). That is,

T(P) = P +

Or T(x, y) = (x, y) + (h, k) = (x + h, y + k ).
In this case, =(h,k) is called a translation vector.