Perpendicular bisector is a line or a ray which cuts another line segment into two equal parts at 90 degree. Bisector is simply a line or a ray which cuts another line segment into two equal parts. In the below image, AB is the perpendicular bisector of the line segment PQ and F is the midpoint of the line segment PQ.
Lets find it with points P(5,7), Q(6,6). Consider the co-ordinates of the points P and Q to be x1,y1 and x2,y2 respectively. We need to calculate the midpoints of the line PQ, which is F, and the slope to find the equation of the perpendicular bisector.
Lets calculate the midpoint of the line which is the average of the x and y co-ordinates. Midpoint of a line = x1+x2/2, y1+y2/2 Midpoint of PQ = 5+6/2, 7+6/2 = (11/2, 13/2)
Next, we need to find the slope of the line PQ using the formula y2-y1/x2-x1. Kindly note that the slope is represented by the letter 'm'. Slope of PQ (m) = 6-7/6-5 = -1.
Now, lets calculate the slope of the perpendicular bisector (AB) of the line PQ. The slope of the perpendicular bisector = -1/slope of the line. Therefore for AB= -1/-1 = 1
Once we find the slope as above, we can find the equation with the slope and the midpoints. Lets find the equation of the AB with midpoints (11/2,13/2) and the slope 1. Formula to find the equation y-y1 = m(x-x1) y-13/2 = 1(x-11/2) By solving the above, we get the equation -x + y = 1. This is the perpendicular bisector equation (AB) of the line PQ.
This tutorial helps to learn the definition and the calculation of perpendicular bisector of a line segment with example.