what is a translation in math

In mathematics, a translation is a transformation that moves a shape left, right, up, or down without changing its size or shape. This means that the original and translated shapes are congruent to each other. A translation preserves the length of the object and is an example of an isometry, which is a transformation that maintains distance. For example, a figure can be translated by a certain number of units horizontally and/or vertically. The general form of a function after translation is (f(x) = f(x + k) + C), where (k) represents the horizontal translation and (C) represents the vertical translation. All points on the shape are shifted by the same number of units during a translation