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The locus of a point which is collinear with the points (1,2) and (–2,1) is x–3y+c = 0 then c =_____

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answer is A.

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Detailed Solution

$A = (1, 2), B = (- 2, 1)$

Equation of AB is $y - y_{1} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} (x - x_{1})$

$y - 2 = \frac{1 - 2}{- 2 - 1} (x - 1) \Rightarrow - 3 y + 6 = - x + 1 \Rightarrow x - 3 y + 5 = 0$

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