Question

Answer the following question:

Line through A(h, 3) and B(4, 1) intersect the line 7x − 9y − 19 = 0 at right angle Find the value of h

Answer 1

Given, A(h, 3) and B(4, 1)

∴ Slope of AB (m₁) = `(1 - 3)/(4 - "h")`

∴ m₁ = `2/("h" - 4)`

Slope of line 7x − 9y − 19 = 0 is m₂ = `7/9`

Since line AB and line 7x − 9y − 19 = 0 are perpendicular to each other,

m₁ x m₂ = −1

∴ `2/("h" - 4) xx 7/9` = −1

∴ 14 = 9(4 − h)

∴ 14 = 36 − 9h

∴ 9h = 22

∴ h = `22/9`