Let  $A\left(7,5\right)$ and $B\left(1,2\right)$ are any two points. The ratio in which the foot of the perpendicular from  $P\left(2,3\right)$ to the line $AB$  divides it is 

$\text{ The slope of }AB\text{ is }m=\frac{2-5}{1-7}=\frac{1}{2}$

$\text{ The equation of the line perpendicular to }AB\text{ and passing through the point }P(2,3{)}_i$

$\begin{array}{c}y-3=-2\left(x-2\right)\\ y-3=-2x+4\\ 2x+y-7=0\end{array}$

$\text{ The ratio of the line segment joining two points }A,B\text{ divided by the line }L=0\text{ is }-\frac{L_A}{L_B}$

$\text{ Hence, the ratio of line segment joining points }A(7,5)\text{ and }B(1,2)\text{ is divided by the line }$

$2x+y-7=0\text{ is }-\frac{L_A}{L_s}=-\frac{2\left(7\right)+5-7}{2\left(1\right)+2-7}=\frac{12}{3}=4$

$\text{ Therefore, the ratio is }4:1$