Find the equation of the perpendicular bisector of the line segment joining the points $(3, 4)$ and $(- 1, 2)$ .

$2 y - x = 5$

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$y - x = 5$

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$y + 2 x = 5$

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$3 y - 2 x = 5$

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Solution

The correct option is C
$y + 2 x = 5$

Midpoint of the points $(3, 4)$ and $(- 1, 2)$

$= (\frac{3 - 1}{2}, \frac{4 + 2}{2}) = (1, 3)$

Slope of a line joining points $(3, 4)$ and $(- 1, 2)$ $= \frac{2 - 4}{- 1 - 3} = \frac{1}{2}$

Slope of the required line = $- 2$
[as they are perpendicular]

So, equation of required line is $(y - 3) = (- 2) (x - 1)$

$\Rightarrow y - 3 = - 2 x + 2$

$\Rightarrow 2 x + y = 5.$

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