Question:
Suppose that the points $(h, k),(1,2)$ and $(-3,4)$ lie on the line $\mathrm{L}_{1}$. If a line $\mathrm{L}_{2}$ passing through the points $(h, k)$ and $(4,3)$ is perpendicular to $\mathrm{L}_{1}$, then $\frac{\mathrm{k}}{\mathrm{h}}$ equals :
Correct Option: , 3
Solution:
equation of $L_{1}$ is
$y=-\frac{1}{2} x+\frac{5}{2}$ .........(1)
equation of $\mathrm{L}_{2}$ is
$y=2 x-5$ ..........(2)
by $(1)$ and $(2)$
$x=3$
$\mathrm{y}=1 \Rightarrow \mathrm{h}=3, \mathrm{k}=1$
$\frac{\mathrm{k}}{\mathrm{h}}=\frac{1}{3}$