CAT 2015 Quantitative Ability

Other two vertices will make two right angled triangles with AB as the common hypotenuse. So they must lie on the circle with AB as the diameter and O as the centre. Radius of that circle will be 5 units. There will be 5 such pairs in which both the coordinates are integers.
[(5,0), (-5,0)] ,
[(-4,3), (4,-3)] ,
[(-3,4), (3,-4)] ,
[(-3,-4),(3,4)] and
[(0,5), (0, -5)]