Translation is the straight line movement of an object from its original position to another position at a given distance and direction.
Let 
be the input vertex and
be
the shifts in x and y directions, respectively.
Recall the equation of transformation
Q = P M + tr . M is an
identity matrix for translation.
Therefore, the translated vertex is given by
For example, let 
and 
. The
translation of a square is shown in the figure below.
Thus two objects can be translated by adding the translation
vector to the coordiantes of each vertex (endpoint).
A homogenous coordinate is appended to each end point.
To translate a circle or an ellipse, its center coordinates
are translated first, and redrawn in the new location.
Translation can be represented in matrix form as
The inverse of translation is given by
, and shifts
, objects can be translated by
adding the translation vector to the coordinates of each
end point.
With the homogenous coordinate
appended to each point, 
It can also be represented in the matrix form
Translation of a unit cube is shown in the figure below.
The inverse translation produces translation in the opposite direction. The inverse of three dimensional transformation is given by
The product of translation matrix and its inverse is an identity matrix