Question

A line passing through the points (a, 2a) and (- 2, 3) is perpendicular to the line 4a + 3y + 5 = 0. Find the value of a.

Answer 1

Let m₁ be the slope of the joining at the points (a, 2a) and (-2, 3), then
m₁ = `(2a - 3)/(a + 2)`
Also slope of the line 4x + 3y + 5 = 0.
m₂ = `-(4)/(3)`
Since, both the line are perpendicular.
So, m₁m₂ = -1
⇒ `(2a - 3)/(a + 2) xx ((-4))/(3)` = -1
⇒ 8a - 12 = 3a + 6
⇒ 8a - 3a = 18
⇒ 5a = 18
⇒ a = `(18)/(5)`
⇒ a = `3(3)/(5)`.