Translation
Definitions
When an object is slid without rotation, all its points are moved according to a vector. This vector defines a direction and a magnitude.
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 point \(M\) is moved to point \(M'\) by sliding along the direction and magnitude 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 translation of all its points.