Perpendicular Bisector

A perpendicular bisector is a line that bisects a line segment and is perpendicular to the line segment. In manipulative 1, line segment AB is the line segment being bisected. The red line is the perpendicular bisector. Point C is the midpoint of line segment AB. Click on the blue points in manipulative 1 and drag them to change the figure. To reset manipulative 1 back to its original configuration, click on the reset button () in the manipulative.

Each point on a perpendicular bisector are the same distance from the endpoints. Since all points on a circle are the same distance from the center of the circle, two circles of the same size can be used to find a perpendicular bisector.

In manipulative 2, point D is the same distance from the center of each of the circles, meaning AD ≡ BD. As the radius AD changes, the points D and E are always on the perpendicular bisector. Click on point D and drag it to trace the perpendicular bisector.

The perpendicular bisectors of the sides of a triangle meet at the circumcenter of the triangle.

The perpendicular bisectors of the sides of a triangle intersect at a point called the circumcenter of the triangle.

The equation of a perpendicular bisector can be calculated for a given line segment with end points (x₁,y₁) and (x₂,y₂). This demonstration will show how to calculate the equation of a perpendicular bisector in point slope form. Click on the points in manipulative 4 and drag them to change the figure.

Step	Equation	Description
1		First calculate the location of midpoint.
2		Calculate the slope of the line segment AB.
3		Calculate the slope of the perpendicular line using the slope of line segment AB.
4		Put the slope of the perpendicular line and the coordinates of the midpoint into and equation in point slope form.
Table 2: Calculating the equation of a perpendicular bisector