Question

Find the equation of the straight line perpendicular to 5x − 2y = 8 and which passes through the mid-point of the line segment joining (2, 3) and (4, 5).

Answer 1

The line perpendicular to 5x − 2y = 8 is $2x+5y+\lambda =0$

$\mathrm{Coordinates}\mathrm{of}\mathrm{the}\mathrm{mid}\mathrm{points}\mathrm{of}\left(2,3\right)\mathrm{and}\left(4,5\right)=\left(\frac{2+4}{2},\frac{3+5}{2}\right)$

= (3,4)

$$\begin{gathered} \therefore 6+20+\lambda =0 \\ \Rightarrow \lambda =-26 \end{gathered}$$

Substituting the value of $\lambda$, we get $2x+5y-26=0$, which is equation of the required line.