Answer :
[tex]\ell_1[/tex] and [tex]\ell_2[/tex] are parallel to one another with slope 1. Any line with slope -1 is perpendicular to both of these lines, the simplest being [tex]y=-x[/tex].
This perpendicular line intersects [tex]\ell_1[/tex] and [tex]\ell_2[/tex] at the points (5/2, -5/2) and (1/2, -1/2), respectively.
The distance between [tex]\ell_1[/tex] and [tex]\ell_2[/tex] is the same as the distance between these two intersections:
[tex]\sqrt{\left(\dfrac52-\dfrac12\right)^2+\left(-\dfrac52+\dfrac12\right)^2}=2\sqrt2\approx\boxed{2.8}[/tex]