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(A) The right bisector of a line segment passes through the midpoint of the segment and is perpendicular to it.The endpoints of the line segment are $

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$2x + y = 5$

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(A) The right bisector of a line segment passes through the midpoint of the segment and is perpendicular to it.The endpoints of the line segment are $A(3, 4)$ and $B(-1, 2)$.The midpoint of $AB$ is $\left(\frac{3-1}{2}, \frac{4+2}{2}\right) = (1, 3)$.The slope of $AB$ is $m_{AB} = \frac{2-4}{-1-3} = \frac{-2}{-4} = \frac{1}{2}$.The slope of the perpendicular bisector is $m = -\frac{1}{m_{AB}} = -\frac{1}{1/2} = -2$.The equation of the line passing through $(1, 3)$ with slope $-2$ is given by $(y - 3) = -2(x - 1)$.$y - 3 = -2x + 2$$2x + y = 5$.

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

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