Question

The line through A (- 2, 3) and B (4, b) is perpendicular to the line 2a – 4y = 5. Find the value of b.

Answer 1

Slope of AB = `(b - 3)/(4 + 2)`
m₁ = `(b - 3)/(6)`
2x - 4y = 5
⇒ 4y = 2x - 5
⇒ y = `(1)/(2) x - (5)/(4)`
slope(m₂₎ = `(1)/(2)`
Since both lines are perpendicular to each other
so, m₁·m₂ = -1
`(b - 3)/(6).(1)/(2)` = -1
b - 3 = -12
b = -9.