If P(x, y) is equidistant from the points

Let the point $P(x, y)$ be equidistant from the points $A(7,1)$ and $B(3,5)$.

Then,

$P A=P B$

$\Rightarrow P A^{2}=P B^{2}$

$\Rightarrow(x-7)^{2}+(y-1)^{2}=(x-3)^{2}+(y-5)^{2}$

$\Rightarrow x^{2}+y^{2}-14 x-2 y+50=x^{2}+y^{2}-6 x-10 y+34$

$\Rightarrow 8 x-8 y=16$

$\Rightarrow x-y=2$