Question

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.

Answer 1

Let the slope of line AB passing through points A(h, 3), B(4, 1) be,

`"m"_1 = (1 - 3)/(4 - "h") = 2/("h" - 4)`

equation of second line

7x − 9y − 19 = 0

or y = `7/9"x" - 19/9`

∴ Slope of the second line, m₂ = `7/9`

Since, both lines intersect each other at right angles,

∴ m₁m₂ = –1

= `2/("h" - 4) xx 7/9 = -1`

14 = –9(h – 4) = –9h + 36

∴ 9h = 36 – 14 = 22

h = `22/9`