IGCSE Distance, Midpoint and Gradient: Complete Guide for Cambridge IGCSE Mathematics

IGCSE distance, midpoint and gradient are essential coordinate geometry topics in Cambridge IGCSE Mathematics that appear in both Paper 2 and Paper 4. Mastering distance formula, midpoint formula, and gradient formula is essential for solving coordinate geometry problems.

This comprehensive IGCSE distance, midpoint and gradient guide covers everything you need to know, including calculating distances, finding midpoints, calculating gradients, worked examples, common exam questions, and expert tips from Tutopiya’s IGCSE maths tutors. We’ll also show you how to avoid the most common mistakes that cost students valuable marks.

🎯 What you’ll learn: By the end of this guide, you’ll know how to calculate distances between points, find midpoints, calculate gradients, and apply these skills to solve problems in IGCSE exams.

Already studying with Tutopiya? Practice these skills with our dedicated IGCSE Algebra practice deck featuring exam-style questions and instant feedback.

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Why IGCSE Distance, Midpoint and Gradient Matter

IGCSE distance, midpoint and gradient are essential coordinate geometry topics. Here’s why they’re so important:

• High frequency topic: These formulas appear regularly in IGCSE maths papers
• Foundation skill: Essential for coordinate geometry and line equations
• Exam weight: Typically worth 5-8 marks per paper
• Real-world applications: Used in mapping, navigation, and geometry
• Problem-solving skills: Develops coordinate geometry understanding

Key insight from examiners: Students often make errors with the formulas or confuse distance and midpoint. This guide will help you master these systematically.

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Understanding Distance, Midpoint and Gradient

These are fundamental coordinate geometry formulas for working with points and lines.

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Distance Formula

Distance between two points: d = √[(x₂ - x₁)² + (y₂ - y₁)²]

Example 1: Find the distance between A(2, 3) and B(5, 7)

Solution: d = √[(5 - 2)² + (7 - 3)²] = √[3² + 4²] = √[9 + 16] = √25 = 5

Answer: 5 units

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Midpoint Formula

Midpoint: ((x₁ + x₂)/2, (y₁ + y₂)/2)

Example 2: Find the midpoint of A(2, 3) and B(8, 9)

Solution: Midpoint = ((2 + 8)/2, (3 + 9)/2) = (10/2, 12/2) = (5, 6)

Answer: (5, 6)

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Gradient Formula

Gradient (slope): m = (y₂ - y₁)/(x₂ - x₁)

Example 3: Find the gradient of the line through A(1, 2) and B(4, 8)

Solution: m = (8 - 2)/(4 - 1) = 6/3 = 2

Answer: 2

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Parallel and Perpendicular Lines

Parallel lines: Same gradient (m₁ = m₂) Perpendicular lines: m₁ × m₂ = -1

Example 4: A line has gradient 3. Find the gradient of a perpendicular line.

Solution: If m₁ = 3, then 3 × m₂ = -1 m₂ = -1/3

Answer: -1/3

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Common Examiner Traps

• Formula errors - Remember correct formulas and order of operations
• Sign errors - Watch positive/negative signs carefully
• Confusing formulas - Distance uses squares, midpoint uses averages

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Practice Questions

Question 1

Find the distance between (0, 0) and (3, 4)

Solution: d = √[(3 - 0)² + (4 - 0)²] = √[9 + 16] = 5

Answer: 5 units

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Tutopiya Advantage: Personalised IGCSE Distance, Midpoint and Gradient Coaching

• Live whiteboard walkthroughs of coordinate geometry problems
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• Analytics dashboard so parents see accuracy by topic
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📞 Ready to turn shaky coordinate geometry skills into exam-ready confidence? Book a free IGCSE maths trial and accelerate your revision plan.

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Frequently Asked Questions About IGCSE Distance, Midpoint and Gradient

What is the distance formula?

Distance formula: d = √[(x₂ - x₁)² + (y₂ - y₁)²] finds the distance between two points.

What is the midpoint formula?

Midpoint formula: ((x₁ + x₂)/2, (y₁ + y₂)/2) finds the point halfway between two points.

What is the gradient formula?

Gradient formula: m = (y₂ - y₁)/(x₂ - x₁) finds the slope of a line.

How do I find perpendicular gradients?

If two lines are perpendicular, their gradients multiply to -1: m₁ × m₂ = -1.

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Related IGCSE Maths Resources

Strengthen your IGCSE Mathematics preparation with these comprehensive guides:

• IGCSE Equation of a Line: Complete Guide - Master line equations
• IGCSE Coordinate Geometry: Complete Guide - Master coordinate geometry
• IGCSE Maths Revision Notes, Syllabus and Preparation Tips - Complete syllabus overview, topic breakdown, and revision strategies
• IGCSE Past Papers Guide - Access free IGCSE past papers and exam resources

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Next Steps: Master IGCSE Distance, Midpoint and Gradient with Tutopiya

Ready to excel in IGCSE distance, midpoint and gradient? Our expert IGCSE maths tutors provide:

• Personalized 1-on-1 tutoring tailored to your learning pace
• Exam-focused practice with real Cambridge IGCSE past papers
• Interactive whiteboard sessions for visual learning
• Progress tracking to identify and strengthen weak areas
• Flexible scheduling to fit your revision timetable

Book a free IGCSE maths trial lesson and get personalized support to master distance, midpoint and gradient and achieve your target grade.

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