Write an equation of the perpendicular bisector of the line segment whose endpoints are (−1,1) and (7,−5)

The equation is

Explanation:

We have to first find the mid-point of the segment, the formula for which is

So, the midpoint will be

                                  =

It is the point at which the segment will be bisected.

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

The slope is =

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

To write an equation, substitute the values in y = mx + c

WHere,

y = -1

x = 3

m = 3/2

Solving for c:

Thus, the equation becomes:

step-by-step explanation:

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