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

Answer

2x+y=5

Explanation

The right bisector of a line segment bisects the line segment at `90^(@)`.
The endpoints of the line segment are given as A(3,4) and B(-1,2).
Accordingly, the midpoint of AB is
`((3-1)/(2), (4+2)/(2)) -= (1,3)`
`"Slope of AB" = (2-4)/(-1-3) = (-2)/(-4) = (1)/(2)`
`therefore "Slope of the line perpendicular to AB" = -(1)/((1//2)) =-2`
The equation of the line passing through (1,3) and having a slope of -2 is.
(y-3) = -2(x-1)
or 2x+y=5