How do you find the equation of a perpendicular bisect or of a line segment?

You can take apart the word ‘perpendicular bisector’:

Perpendicular means at a right angle to the line.

So you would find the gradient of your line segment, assuming you were given two points along the line. Then find the negative reciprocal of this gradient to get your new gradient.

Bisector means cut in half.

So you find the midpoint of your line segment.

Now, substitute the midpoint coordinate and your new gradient into the equation of a straight line.

Hope this helps :D