Question

basic defination of translation

Answer 1

The movement of an object in space independent of rotation.
NOTE: This could be 2D or 3D OR ND space where N is an integer

Answer 2

\[\left[\begin{matrix}1 & 0 & a\\ 0 & 1 & b \\ 0 & 0 & 1\end{matrix}\right] * \left(\begin{matrix}x \\ y\end{matrix}\right) = \left(\begin{matrix}a+x \\ b+y\end{matrix}\right)\]