Identify the equation in point-slope form for the perpendicular bisector of the segment with endpoints J(−24,−4) and K(−4,6).

Question

please walk me through how to do this so I can do it on my own next time :) thank you!

Answer 1

The slope of the segment JK is (6--4)/(-4--24) = 10/20 = 1/2

The slope of the perpendicular bisector is the negative reciprocal of -2/1 = -2

Since it is the perpendicular bisector that line contains the midpoint of segment JK = ((-24 + -4)/2, (-4+6)/2) = (-14,1)

point-slope form is y-y1 = m(x-x1).

m is -2, x1 = -14 and y1 = 1

so y-1 = -2(x+14)