Question

Find anequation for the perpendicular bisector of the line segment whose endpoints are(3, -1) and (-9,5).

Answer 1

The perpendicular bisector goes through the midpoint.

What is the midpoint of the 2 points?

We simply add up the x points and divide by 2. Then we add up the y points and divide by 2.

So,

Midpoint is:

$(\frac{3-9}{2},\frac{-1+5}{2})=(-3,2)$

Also, the perpendicular bisector's slope is the negative reciprocal of the line's slope.

The slope of the line is change in y points divided by change in x points.

Slope =

$\frac{5--1}{-9-3}=\frac{5+1}{-12}=\frac{6}{-12}=-\frac{1}{2}$

The slope (m) of the perpendicular line (negative reciprocal) is basically:

$2$

Equation of line is:

$y-y_1=m(x-x_1)$

m is the slope (what we got "2")

x1 and y1 are the respective point where it passes through (which is the midpoint, which is (-3,2)

So, equation of perpendicular bisector is:

$\begin{gathered} y-y_1=m(x-x_1) \\ y-2=2(x+3) \\ y=2x+6+2 \\ y=2x+8 \end{gathered}$