What is a Perpendicular Bisector?
A perpendicular bisector is a line that divides a line segment into two equal parts at a 90-degree angle. It has significant applications in geometry, construction, and various mathematical concepts.
Key Characteristics:
- Equidistant Points: Every point on the perpendicular bisector is equidistant from the endpoints of the line segment it bisects.
- Construction: To construct a perpendicular bisector:
- Place the compass point on one endpoint and draw an arc above and below the line segment.
- Without changing the compass width, repeat from the other endpoint.
- The intersection points of the arcs determine the line that is the perpendicular bisector.
- Equation in Coordinate Geometry: For a line segment with endpoints (x1, y1) and (x2, y2):
- The midpoint can be found using ((x1 + x2)/2, (y1 + y2)/2).
- The slope of the original segment is m = (y2 - y1) / (x2 - x1), and the perpendicular slope is -1/m.
Applications:
- Geometry: Used in triangle constructions, such as determining circumcenters.
- Real-life Applications: Employed in fields like engineering and architecture for ensuring structural symmetry.
- Mathematical Proofs: Serves as a foundation for various geometric proofs and theorems.
Understanding the concept of perpendicular bisectors is essential for students studying geometry, as it enhances problem-solving skills and geometric reasoning.

a line or ray which intersect any line segment at 90°