Question

Enter an equation in point-slope form for the perpendicular bisector of the segment with endpoints (−3, 7) and (1, −5).

The point-slope equation of the perpendicular bisector is .

Answer 1

First find the slope of the line segment joining the points.
Slope = ((-5)-7)/(1-(-3)) = -3

The slope of any perpendicular to the line is 1/3

Find the midpoint of the line segment by taking the average of the coordinates.
x-coord of midpoint = (-3+1)/2 = -1
y-coord of midpoint = (7-5)/2 = 1
Midpoint : (-1,1)

Point-slope equation for line of slope 1/3 that passes through (-1,1):
y-1 = (1/3)(x+1)