Find an equation for the perpendicular bisector of the line segment whose endpoints are (1,6) and (-9,-2)

Answer 1

(1,6), (-9,-2) have a line through them with slope = (6+2)/(1+9) = 8/10=4/5

a perpendicular line has slope = the negative inverse= -5/4

perpendicular bisector goes through the midpoint =(-4,2)

(1,6),(-9,-2) has midpoint that's the average of x coordinates, (1-9)/2 = -4, and average of y coordinates: (6-2)/2 = 2

the equation of the perpendicular bisector is

y=(-5/4)x + b, solve for b by plugging in the point (-4,2)

2 = (-5/4)(-4) +b

2 = 5+b

b= -3

y = (-5/4)x -3 in slope intercept form

or

5x+4y = -12 in standard form

5x+4y+12=0 in general form

Answer 2

Slope of given segment is (-2 -6) / (-9 - 1) = 4/5

Midpoint of given segment is (-4, 2)

Perpendicular bisector passes through (-4,2) and has slope -5/4

Use the point-slope form to write your equation.