Show that $\lbrace (q,0) : q \in \mathbb{Q} \rbrace $ is a closed subset of the Moore Plane

Question

Let $\Gamma$ be the Moore Plane, I have to show that the set $\lbrace (q,0) : q \in \mathbb{Q} \rbrace $ is closed.

I have tried to prove it by trying to find a neigbourhood of every point in the complimentary, but these neigbourhoods aren't contained in the complimentary, since $\mathbb{Q}$ is dense, I don't know how to start to prove it then.

Thanks in advance!