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

Solution:

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

m₁ = (1 - 3)/(4 - h) = - 2/(4 - h)

The slope of the line 7x – 9y – 19 = 0 or y = 7/9x - 19/9 is m\(_2\) = 7/9

It is given that the two lines are perpendicular.

Therefore,

⇒ m\(_1\) x m\(_2\) = - 1

⇒ - 14/(36 - 9h) = - 1

⇒ 14 = 36 - 9h

⇒ 9h = 36 - 14

h = 22/9

Thus, the value of h = 22/9

NCERT Solutions Class 11 Maths Chapter 10 Exercise 10.3 Question 10

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.

Summary:

If the line through the points (h, 3) and (4, 1) intersects the line 7x – 9y – 19 = 0 at right angle then the value of h is 22/9