general topology – quotient of $ R ^ 2 $

Consider $ X $=$ R ^ 2 $ and leave A $ in X $ to be A = {$ (- 1.0), ($ 1.0)}. Now consider the space of the quotient $ {X} / {A} $.

Is it Hausdorff? Connected? Compact?

My answer: the projection of $ X $ at $ A $ is surjective and continuous, $ X $ is connected and so is $ {X} / {A} $.

The projection of the open cover of $ X $ ball compound centered on $ (0,0) $ is an open cover of $ X / A $ as they are both open and saturated. We can not extract finite under-coverage and because of that $ {X} / {A} $ is not compact.

Honestly, I'm not sure of the evidence about compactness and I'm stuck with the Hausdorff question. If I could show that the projection is open, I could work from there. Working with intervals has left a proof that I am not 100% sure.

Thank you in advance for your help.