Answer
$I = 2.0~kg~m^2$
Work Step by Step
The two particles on the rotation axis are a distance of $~~0~~$ from the rotation axis.
We can find the distance of the other two particles:
$r = \sqrt{(1.0~m)^2+(1.0~m)^2} = \sqrt{2.0}~m$
We can find the rotational inertia:
$I = 2\times (0.50~kg)(0)^2+2\times (0.50~kg)(\sqrt{2.0}~m)^2$
$I = 2.0~kg~m^2$
