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.

Question

Philoid · Accepted Answer

Let the slope of the line passing through (h, 3) and (4, 1) be m₁

Then,

Let the slope of line 7x – 9y – 19 = 0 be m₂

⇒ 7x – 9y – 19 = 0

Since, the given lines are perpendicular

Therefore, m₁ × m₂ = -1

⇒ -14 = -1 × (36 – 9h)

⇒ 36 – 9h = 14

⇒ 9h = 36 – 14

⇒ h = 22/9

∴ h = 22/9