An integer point has integer coordinates. Also call point (x,y) different if all the distances from (x,y) to integer points are different.
Show that (3/4, 2/5) is not different
So you want to show that there exist points and , either or , such that .
I recommend starting by squaring both sides. You can then write the equation in terms of and . Obviously one solution will be and but there is another solution. Find it.