Suppose I have two lattices of points $A=\{a_1,\dots,a_n\}\subseteq\mathbb{R}^2$ and $B=\{b_1,\dots,b_n\}\subseteq\mathbb{R}^2$ and I calculate the best affine transformation $A\to B$ in the least squares sense (an account of this may be found in hrcak.srce.hr/file/1425). In particular, the translational part of the transformation is a vector $v\in\mathbb{R}^2$. Could I retrieve the same vector by taking the vector that takes the average of $A$ into that of $B$, i.e. $(\sum_{i=1}^n(b_i - a_i))/n$?
Thanks!