Question

How do I find the equation of the perpendicular bisector of the line segment whose endpoints are (-4, 8) and (-6, -2) using the Midpoint Formula?

Answer 1

`y=-1/5x+2`

Explanation:

First, you must find the midpoint of the segment, the formula for which is `((x_1+x_2)/2,(y_1+y_2)/2)`. This gives `(-5, 3)` as the midpoint. This is the point at which the segment will be bisected.

Next, since we are finding a perpendicular bisector, we must determine what slope is perpendicular to that of the existing segment. To determine the segment's slope, we use the slope formula `(y_2-y_1)/(x_2-x_1)`, which gives us a slope of `5`.

Perpendicular lines have opposite and reciprocal slopes. The opposite reciprocal of `5` is `-1/5`.

We now know that the perpendicular travels through the point `(-5,3)` and has a slope of `-1/5`.

Solve for the unknown `b` in `y=mx+b`.

`3=-1/5(-5)+b=>3=1+b=>2=b`

Therefore, the equation of the perpendicular bisector is `color(blue)(y=-1/5x+2)`.