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?

1 Answer
mason m
Nov 14, 2015

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).

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