Question

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

Answer 1

The slope of the line passing through points $(h,3)$ and $(4,1)$ is :

$m_1=\frac{1-3}{4-h}=\frac{-2}{4-h}$

The slope of the line $7x-9y-19=0$ is $m_2=\frac{7}{9}$

Given that two lines are perpendicular.

Therefore,

$m_1\times m_2=-1$

$\left(\frac{-2}{4-h}\right)\times \frac{7}{9}=-1$

$14=36-9h$

$9h=22$

$h=\frac{22}{9}$