Equation of a perpendicular bisector

Question

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

Answer 1

First find slope of line segment:

(6-2)/(1-9) = -4/8 = -1/2

Slope of perpendicular bisector is negative reciprocal of line segment or 2.

Find midpoint of line segment where perpendicular bisector intercepts line segment:

(9+1 / 2, 2 + 6/ 2) = (5,4)

equation of line is y = mx + b, where m is slope and b is y -intercept

we have found m = 2, so

y = 2x + b

We know perpendicular bisector contains (5,4), so substitute those for x,y in above equation and solve for b:

4 = 2(5) + b

b = -6

so equation is

y = 2x - 6