Skip to content
IGCSEMath.com.my
Extended Only Coordinate Geometry

Perpendicular Bisector for IGCSE Maths

Finding the equation of the perpendicular bisector of a line segment. This subtopic is part of Coordinate Geometry in the Cambridge IGCSE Mathematics 0580 syllabus (Extended tier only). Understanding

What You Need to Know

Finding the equation of the perpendicular bisector of a line segment. This subtopic is part of Coordinate Geometry in the Cambridge IGCSE Mathematics 0580 syllabus (Extended tier only). Understanding perpendicular bisector is essential for achieving a strong grade in your IGCSE Maths exam.

Understanding Perpendicular Bisector

The perpendicular bisector of a line segment AB is the line that (1) passes through the midpoint of AB and (2) is perpendicular to AB. Any point on the perpendicular bisector is equidistant from A and B — this makes it a key construction for loci problems. In IGCSE Extended, students are asked to find its equation analytically using the midpoint formula and the perpendicular gradient rule.

Step-by-Step Method

  1. 1

    Find the midpoint M

    M = ((x₁+x₂)/2, (y₁+y₂)/2). This is the point the perpendicular bisector passes through.

  2. 2

    Find the gradient of AB

    m_AB = (y₂−y₁)/(x₂−x₁).

  3. 3

    Find the perpendicular gradient

    m_perp = −1/m_AB (negative reciprocal).

  4. 4

    Form the equation

    Use y − y_M = m_perp(x − x_M), then rearrange into y = mx + c form.

  5. 5

    Verify

    Check that M lies on your line, and that the gradients multiply to −1.

Worked Example

Question

Find the equation of the perpendicular bisector of the line segment joining A(2, 6) and B(8, 2).

Solution

Step 1: Midpoint M = ((2+8)/2, (6+2)/2) = (5, 4). Step 2: Gradient of AB = (2−6)/(8−2) = −4/6 = −2/3. Step 3: Perpendicular gradient = 3/2. Step 4: Equation through (5, 4) with gradient 3/2: y − 4 = (3/2)(x − 5) y − 4 = (3/2)x − 15/2 y = (3/2)x − 15/2 + 4 y = (3/2)x − 7/2 Answer: y = (3/2)x − 3.5 (or 2y = 3x − 7)

Exam Tips for Perpendicular Bisector

  • The perpendicular bisector must pass through the MIDPOINT — not through A or B.
  • If asked to show a point lies on the perpendicular bisector, substitute it into your equation — equality confirms it.
  • The perpendicular bisector is the locus of points equidistant from A and B — useful in circle and loci questions.
  • Use fractions, not decimals, for gradients and intercepts unless the question requires decimal form.

Practice Questions

Q1: Find the equation of the perpendicular bisector of the segment joining P(1, 3) and Q(5, 7).

Show hint

Midpoint = (3, 5). Gradient PQ = 1. Perpendicular gradient = −1.

Q2: Points A(0, 4) and B(6, 0) are on a circle. Show that the perpendicular bisector of AB passes through (5, 5).

Show hint

Find the perpendicular bisector equation and substitute (5, 5) to verify it satisfies the equation.

Q3: The perpendicular bisector of AB passes through the point (7, 3). A has coordinates (1, 1). Find the coordinates of B.

Show hint

Set up: midpoint must lie on the line, and the gradient condition must hold. Use the midpoint and gradient to form two equations.

Frequently Asked Questions

What is perpendicular bisector in IGCSE Maths?

Finding the equation of the perpendicular bisector of a line segment.

Is perpendicular bisector in the Core or Extended syllabus?

Perpendicular Bisector is part of the Extended only syllabus for IGCSE Mathematics 0580.

How do I revise perpendicular bisector effectively?

Start with the revision notes to understand key concepts, then work through the worked examples step by step. Finally, practise past paper questions under timed conditions. Teacher Rig recommends spending focused revision sessions on perpendicular bisector rather than trying to cover everything at once.

Need Help with Perpendicular Bisector?

Book a free trial class and get personalised support from Teacher Rig.

Book Free Trial WhatsApp Us

More on Coordinate Geometry

Related Subtopics

Explore More

Master Perpendicular Bisector with Expert Help

Book a free 60-minute trial class with Teacher Rig. Get personalised guidance on Coordinate Geometry and every other IGCSE Maths topic.

Book Free Trial WhatsApp Us