Question

A line segment, ST, has endpoints S(4,-3) and T(0,-1). Which of the following equations represents the perpendicular bisector of the line segment?

Answer 1

The slope of the given segment is
m = Δy/Δx = (-1 -(-3))/(0 -4) = 2/-4 = -1/2

The midpoint of the given line is
(S +T)/2 = ((4, -3) +(0, -1))/2 = (4/2 -4/2) = (2, -2)

The slope of the perpendicular line is
-1/m = -1/(-1/2) = 2

So, in point-slope form, the equation of the perpendicular bisector is
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
y +2 = 2(x -2)
This can be rearranged to any of several forms:
y = 2x -6 . . . . . . slope-intercept form
2x -y = 6 . . . . . . standard form