Find an equation for the perpendicular bisector of the line segment whose endpoints
are (-1, -2) and (-5,4).

Step-by-step explanation:

Perpendicular Bisector

It's defined as a line that divides another line into two equal parts. The bisector passes through the midpoint of the line forming any angle, but if that angle is exactly 90°, then the bisector is also perpendicular.

We need to find the equation of the line that divides into equal parts the line with endpoints (-1, -2) and (-5,4) and is perpendicular to it.

First, let's find the slope of the line segment. The slope can be calculated with the formula:

The line for the perpendicular bisector has a slope m2. Two perpendicular lines with slopes m1 and m2 must comply:

Solving for m2:

The equation of the perpendicular bisector has the form:

Now we find the coordinates of the midpoint of the segment:

The midpoint is (-3,1). Using this point will allow us to find the value of b:

Thus, the equation for the perpendicular bisector is

answer: the correct one is a

step-by-step explanation: