A line perpendicular to the line segment joining the points $(7, 3)$ and $(3, 7)$ divides it in the ratio $1:3$, the equation of the line is

Slope of the given line is $\frac{7-3}{3-7}=-1$ and the coordinates of the point which divides the given line segment in the ratio $1:3$ is $\left(\frac{1\times 3+3\times 7}{4},\frac{1\times 7+3\times 3}{4}\right)=(6,4)$

So equation of the line passing through the point (6, 4) and perpendicular to the given line is

$y-4=x-6 \Rightarrow x-y-2=0.$