Question

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

Answer 1

If two lines intersect at right angles, then product of their slope is - 1

Slope of $7x-9y-19=0$ is $m_1=\frac{7}{9}...\left(1\right)$

Slope of line joining $(h,3)$ and $(4,1)=\frac{1-3}{4-h}$

or, $m_2=\frac{2}{h-4}...\left(2\right)$

$m_1\times m_2=-1$

$\frac{7}{9}\times \frac{2}{h-4}=-1$

$14=-9h+36$

$9h=36-14$

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