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Perpendicular Bisector Theorem Calculator

Online perpendicular bisector (number line) calculator. Enter a segment's endpoint coordinates to find the midpoint and learn that bisector points are equidistant from both ends—ideal for geometry.

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Midpoint=(x1+x2)/2; the bisector passes through it at 90°
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Coordinate of one endpoint
Coordinate of the other

📖 Tutorial | Perpendicular Bisector

1. Definition
The perpendicular bisector is the line through the midpoint at 90° to the segment.
2. Formula & Notation
x1, x2Endpoint coordinates
MMidpoint, (x1+x2)/2
3. Properties & Laws
  • Points on it are equidistant from the endpoints;
  • Equidistant points lie on it;
  • Three meet at the circumcenter;
  • It is unique.
4. Steps
  1. Enter endpoint coordinates x1, x2;
  2. Click "Find Midpoint";
  3. Or click "Load Example".
5. Worked Examples
Example: coordinates 2 and 8.
Solution: midpoint = (2+8)/2 = 5.
6. Common Pitfalls
Midpoint is the average;
It must be perpendicular through the midpoint;
Not an angle bisector.

❓ FAQ | Perpendicular Bisector

What is a perpendicular bisector?
The line through the midpoint at 90°.
Its property?
Any point on it is equidistant from the endpoints.
How to test a point is on it?
It is equidistant from the endpoints.
Midpoint of 2 and 8?
5.
Three bisectors of a triangle?
Meet at the circumcenter.
How many per segment?
Exactly one.