Rectangle [tex]$ABCD$[/tex] with coordinates [tex]$A(1,1), B(4,1), C(4,2)$[/tex], and [tex]$D(1,2)$[/tex] dilates with respect to the origin to give rectangle [tex]$A'B'C'D'$[/tex] such that [tex]$\overline{A'B'}=6$[/tex]. What is the scale factor of the dilation?
A. 6
B. 3
C. 2
D. [tex]$\frac{\pi}{2}$[/tex]
E. 4