looking for the intersection point where two lines are perpendicular

Hi all, this is probably a silly problem but I cant find a quick solution to it

I've got two points and I want to find the lines that form a 90º degrees angle having the same intersection point in its perpendicular bisector.

it would be more or less like this drawing

I thought it would be possible with the definition attached, but the thing is that I always get angles like 90,234325313, never 90.0 

the more precision I want the wider has to be the domain, so maybe with a really huge domain I will end up getting close to 90.0...but Im sure it has to be a much better way to do it

thanks