The equation two the perpendicular bisectors of the line segment joining $(1, 2), (3, 4)$ is

2 x - y + 5 =

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x + y - 5 = 0

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3 x - 2 y + 5 = 0

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x + y - 4 = 0

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Solution

The correct option is B $x + y - 5 = 0$
Slope of the line joining the points $(1, 2)$ and $(3, 4)$ -
$m_{1} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{4 - 2}{3 - 1} = \frac{2}{2} = 1$
Therefore,
$m_{1} m_{2} = - 1$
$\Rightarrow m_{2} = \frac{- 1}{m_{1}} = - 1$
Also mid-point of the line joining the points $(1, 2)$ and $(3, 4)$ -
$(h, k) = (\frac{3 + 1}{2}, \frac{4 + 2}{2}) = (2, 3)$ .
Therefore,
Equation of perpendicular bisector $= (y - k) = m_{2} (x - h) = y - 3 = - 1 (x - 2) = y - 3 = 2 - x = x + y - 5 = 0$
Hence the equation of prpendicular bisector is $x + y - 5 = 0$ .

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The equation two the perpendicular bisectors of the line segment joining (1,2),(3,4) is

The equation two the perpendicular bisectors of the line segment joining $(1, 2), (3, 4)$ is