See if two points are on same side of a line in point normal form?

I already have the means to check if two points are on the same side of a plane defined as three points. That is almost always the case that comes up, but in one place all I ever have is a point and a normal to define the plane. I tried to convert the point normal form plane to a triangle, but this method doesn't quite work right. It's not numerically robust. I can see why but fixing it would be iffy and since it's a hacked together means I was hoping to find someone who knows how to do this in the 'right' way.

However, I can't seem to think of a way to check if two points are on the same side or not in that form. I also can't seem to figure out a robust way to put it into 3 point form without going way more elaborate than the problem probably calls for.

So, if someone knows an easy way to accomplish either of these objectives that would be awesome.

Nevermind. I found it was easier and much faster to just convert it to hessian normal form.