Let L be the line passing through the point P(1, 2) such that its...

If $P is the midpoint of the segment between the axes, them point$A\left(2, 0\right)$and$B\left(0, 4\right)$.</p><p>The equation of the line is,$\dfrac{x}{2} + \dfrac{y}{4} = 1$</p><p>or,$2x + y = 4 \ldots \left(1\right)$</p><p>The line perpendicular to it is of form,$x - 2y = k$</p><p>Since it passes through$( - 2, 1 )$,</p><p>$- 2 - 2 = k ⇒ k = - 4$</p><p>$∴$Line is,$x - 2y = - 4 \ldots \left(2\right)$</p><p>Solving \left(1\right)$ and \left(2\right)$we get \left(\dfrac{4}{5}, \dfrac{12}{5}\right)$.