Translation

A translation occurs if all the points forming a particular figure in the Euclidean plain shift by the same distance and direction as defined by the translation vector. A vector  is a quantity that has a magnitude and a direction.

For example, in order to translate a triangle in the plane, points (2,1), (3,4),(4,1), by 4 units to the right and 1 unit upwards; every point forming the triangle will need to move with the same direction and magnitude as the translation vector < 4,1>.  

The algebraic addition of the x component of every point in the figure with the x component of the translation vector and the algebraic addition of the y component of every point in the figure with the y component of the translation vector as shown below will result in the desired translation

The plot of the translation points produces the following figure: