Let L be the line passing through the point P 1 , 2 such that its intercepted segment between the…

If $P$ is the midpoint of the segment between the axes, them point  $A\left(2, 0\right)$ and $B\left(0, 4\right)$.

The equation of the line is, $\frac{x}{2}+\frac{y}{4}=1$

or, $2x+y=4 \dots \left(1\right)$

The line perpendicular to it is of form, $x-2y=k$

Since it passes through $(-2, 1)$,

 $-2-2=k\Rightarrow k=-4$

$\therefore$ Line is, $x-2y=-4 \dots \left(2\right)$ 

Solving $\left(1\right)$ and $\left(2\right)$ we get $\left(\frac{4}{5},\frac{12}{5}\right)$.