Question

The line through the points $(h,3)$ and $(4,1)$ intersects the line $7x-9y-19=0$ at right angle. Then, the value of $h$ is

• A. $\frac{11}{7}$
• B. $\frac{22}{7}$
• C. $\frac{22}{9}$
• D. $\frac{11}{9}$

Answer 1

Answer: (C)

Slope of the line passing through $(h,3)$ and $(4,1)$ is
$m_1=\frac{1-3}{4-h}=\frac{-2}{4-h}\left(\because m=\frac{y_2-y_1}{x_2-x_1}\right)$
Given, equation of line is
$7x-9y-19=0$
$y=\frac{7}{9}x-\frac{19}{9}....$(i)
On comparing Eqs. (i) with $y=mx+c$, we get
$m_2=\frac{7}{9}$
$\because$ The lines are perpendicular to each other.
$\therefore m_1{m}_2=-1$
$\Rightarrow -\frac{2}{4-h}\times \frac{7}{9}=-1$
$\Rightarrow 14=9(4-h)$
$\Rightarrow 14=36-9h\Rightarrow 9h=22$
$\therefore h=\frac{22}{9}$