Translation
What is a Translation?
When an object is slid without turning, all its points are moved in the same way. This movement can be represented by a vector, which gives the direction and the length of the translation.
The cable car \(\textcolor{colorprop}{A'}\) is the image of cable car \(\textcolor{colordef}{A}\) under the translation by vector \(\textcolor{olive}{\vec{v}}\).
The cable car \(\textcolor{colorprop}{A'}\) is the image of cable car \(\textcolor{colordef}{A}\) under the translation by vector \(\textcolor{olive}{\vec{v}}\).
Definition Translation of a Point
The translation of point \(M\) by vector \(\textcolor{olive}{\vec{v}}\) is the point \(M'\) such that \(\overrightarrow{MM'}=\textcolor{olive}{\vec{v}}\): point \(M\) is slid to point \(M'\) following the direction and the length of the vector \(\textcolor{olive}{\vec{v}}\).
Example
Find the coordinates of the image of point \(M\) under a translation by vector \(\textcolor{olive}{\vec{v}}\).
Definition Translation
The translation of an object by vector \(\textcolor{olive}{\vec{v}}\) is the figure obtained by translating all its points by the same vector \(\textcolor{olive}{\vec{v}}\).