If the straight line passing through the points (h, 3)and (4, 1) intersects the line 7x – 9y – 19 = 0 at right angle, then find the value of h.

Given: The straight line passing through the points (h, 3)

and (4, 1) intersects the line 7x – 9y – 19 = 0 at right angle.

As these lines intersect at right angle, they are perpendicular to each other.

When the lines are perpendicular to each other, the product of their slopes is equal to –1.

Slope of the first line passing through the points (h,3) and (4,1)

(here the two points are(x1,y1) and (x2,y2))

Now,

⇒

Slope of the second line 7x – 9y –19 = 0 is

Therefore, product of the slopes is

⇒

⇒

⇒

⇒ 14 = 36–9h

⇒ 9h = 36–14 = 22

⇒