Question

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

Answer 1

Let m₁ be the slope of the line joining the points (a, 2a) and (−2, 3)

$m_1=\frac{3-2a}{-2-a}$

It is given that the line passing through points (a, 2a) and (−2, 3) is perpendicular to the line 4x + 3y + 5 = 0.

$$\begin{gathered} \therefore m_1\times \frac{-4}{3}=-1 \\ \Rightarrow \frac{3-2a}{-2-a}\times \frac{-4}{3}=-1 \\ \Rightarrow 8a-12=3a+6 \\ \Rightarrow a=\frac{18}{5} \end{gathered}$$

Hence, the value of a is $\frac{18}{5}$.