Find an equation for the perpendicular bisector of the line segment whose endpoints are ( 9 , 7 ) (9,7) and ( − 3 , − 5 ) (−3,−5).

Answer 1

The perpendicular bisector of the line segment between (9,7) and (-3,5) will have a slope equal to the negative reciprocal of the slope between those two points and contain the midpoint between those two points.

The slope between those two points is (5-7).(-3-9) = -2/-12 = 1/6

The slope of the line perpendicular that segment will be -6.

The midpoint between those two points is ((9+-3)/2, (7+5)/2) = (3,6)

The formula for the equation of a line is y = mx + b, where m is the slope and b is the y-intercept

For the perpendicular bisector, m = -6. we can substitute (3,6) for (x,y) in the equation to find b:

6 = -6(3) + b

24 = b

so the equation of the perpendicular bisector is:

y = -6x + 24