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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.

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Solution

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

m1=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.

m1×-43=-13-2a-2-a×-43=-18a-12=3a+6a=185

Hence, the value of a is 185.

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