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?
First, you must find the midpoint of the segment, the formula for which is
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
Perpendicular lines have opposite and reciprocal slopes. The opposite reciprocal of
We now know that the perpendicular travels through the point
Solve for the unknown
Therefore, the equation of the perpendicular bisector is