IBMathsDPApplications & Interpretation (AI)HLRevision Notes3. Geometry & TrigonometryGeometry ToolkitPerpendicular Bisectors

Perpendicular Bisectors (DP IB Applications & Interpretation (AI): HL): Revision Note

Written by: Amber

Reviewed by: Dan Finlay

Updated on 27 November 2025

Perpendicular bisectors

What is a perpendicular bisector?

A perpendicular bisector of a line segment is a line that
- is perpendicular to the line segment
- cuts the line segment into two equal halves
The perpendicular bisector goes through the midpoint of the line segment

How do I find the equation of the perpendicular bisector of a line segment?

STEP 1
Find the coordinates of the midpoint of the line segment
- Use the formula $(\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})$
STEP 2
Find the gradient of the line segment
- Use the formula $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

STEP 3
Find the gradient of the perpendicular bisector
- Use the formula $m_{⊥} = - \frac{1}{m}$
STEP 4
Find the equation of the straight line using the gradient and midpoint
- Use the formula $y - y_{1} = m (x - x_{1})$
STEP 5
Rearrange into the required form
- Either $y = m x + c$ or $a x + b y + d = 0$
- These equations for a straight line are given in the formula booklet

Worked Example

Point $A$ has coordinates $(4, - 6)$ and point $B$ has coordinates $(8, 6)$ . Find the equation of the perpendicular bisector to $[AB]$ .

Give your answer in the form $a x + b y + d = 0$ .

Answer:

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