1. 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. In triangle geometry, perpendicular bisectors are used to find the circumcenter - the center of the circle that passes through all three vertices of a triangle.

2. How Does the Calculator Work?

The calculator uses geometric formulas:

Where:

• \( (x_1, y_1) \) — Coordinates of point A
• \( (x_2, y_2) \) — Coordinates of point B
• Midpoint — Center point of segment AB
• Perpendicular Slope — Negative reciprocal of AB's slope

3. Importance of Perpendicular Bisectors

Details: Perpendicular bisectors are fundamental in triangle geometry, used to construct circumcircles, solve geometric problems, and have applications in computer graphics, engineering, and architecture.

4. Using the Calculator

Tips: Enter the coordinates of two points to find the perpendicular bisector of the line segment connecting them. The calculator will provide the midpoint coordinates and the equation of the perpendicular bisector line.

5. Frequently Asked Questions (FAQ)

Q1: What if the line segment is horizontal?
A: The perpendicular bisector will be a vertical line passing through the midpoint.

Q2: What if the line segment is vertical?
A: The perpendicular bisector will be a horizontal line passing through the midpoint.

Q3: Can I use this for three points to find a triangle's circumcenter?
A: Yes, find perpendicular bisectors for two sides and their intersection gives the circumcenter.

Q4: What if the points are identical?
A: The calculator requires distinct points as a line segment cannot be formed with identical points.

Q5: How accurate are the results?
A: Results are calculated with high precision (4 decimal places) for most practical applications.