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

Let A (h,3) and B (4,1) be the given points.

The line 7x − 9y − 19 = 0 can be written as

$y=\frac{7}{9}x-\frac{19}{9}$

So, the slope of this line is $\frac{7}{9}$

It is given that the line joining the points A (h,3) and B (4,1) is perpendicular to the line 7x − 9y − 19 = 0.

$$\begin{gathered} \frac{7}{9}\times \frac{1-3}{4-h}=-1 \\ \Rightarrow 9h-36=-14 \\ \Rightarrow 9h=22 \\ \Rightarrow h=\frac{22}{9} \end{gathered}$$

Hence, the value of h is $\frac{22}{9}$.