J13

Translations
If the object moves in such a way that all its points move through the same distance and
in the same direction, the object is said to have undergone a translation.
Consider a translation from point A to B in the figure below.
If each square is of one unit length, the translation is shown by the vector AB and can be
described as a displacement of 6 units to the right and 4 units upwards. This is written
6
as AB = .
4
When a displacement vector is written in this way it is called a column vector. The
number at the top represents the horizontal displacement and the lower number
represents the vertical displacement.
The figure below shows a displacement from P to Q.
The vector PQ is a displacement of 6 units to the left and 2 units downwards. This is
6
written as PQ = .
2
It is important to note that whenever the displacement is towards the right or upwards, it
is a positive displacement whilst displacement to the left or downwards is negative.
Example