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