Find an equation for the perpendicular bisector of the line segment whose endpoints are (−3,4) and (−7,−6).

Step-by-step explanation:

First, you must find the midpoint of the segment, the formula for which is . This gives you (-5,-1) 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 , which gives us a slope of .

Perpendicular lines have opposite and reciprocal slopes. The opposite reciprocal of is .

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

Solve for in .

Therefore, the equation of the perpendicular bisector is  .