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

A
18/5
B
18
C
5
D
1

Solution:

Slope of the line joining $(a, 2 a), (- 2, 3) is \frac{2 a - 3}{a + 2}$
Slope of the line $4 x + 3 y + 5 = 0 is - 4 / 3$
Product of the slopes $= - 1 - \frac{4}{3} \times \frac{29 - 3}{a + 2} = - 1 \Rightarrow 8 a - 12 = 3 a + 6 \Rightarrow 5 a = 18 \Rightarrow a = \frac{18}{5}$

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