Share '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, nev…