# Suppose that the points $(h,k),(1,2)$ and $\left ( -3,4 \right )$ lie on the line $L_1.$ If a line $L_2$ passing through the points $\left ( h,k \right )$ and $\left ( 4,3 \right )$ is perpendicular to $L_1,$ then $\frac{k}{h}$ equals: Option 1)$\frac{1}{3}$Option 2)$0$Option 3)$3$  Option 4)$-\frac{1}{7}$

Line $L_1$ contain points : $\left ( h,k \right ),(1,2)$ and $\left ( -3,4 \right )$

slope of $L_1=\frac{4-2}{-3-1}=-\frac{1}{2}$

$L_2$ is $\perp$ to $L_1;$ so slope of $L_2$ is $2$

Again; slope of $L_1=\frac{k-2}{h-1}=-\frac{1}{2}$

$\Rightarrow 2k-4=-h+1\Rightarrow h+2k=5\cdots (1)$

Line $L_2$ contains point : $\left ( h,k \right ),(4,3)$

Slope of $L_2=\frac{k-3}{h-4}=2\Rightarrow k-3=2h-8$

$k=2h-5\cdots (II)$

solve (1) and (2), $(h,k)=(3,1)$

Option 1)

$\frac{1}{3}$

Option 2)

$0$

Option 3)

$3$

Option 4)

$-\frac{1}{7}$

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