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Distance Formula

ICSE · Class 9 · Mathematics

Complete topic list for Distance Formula in ICSE Class 9 Mathematics. Key concepts, sub-topics, and what to focus on for board exams.

33 questions24 flashcards5 concepts

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A 3D diagram showing three points A, B, and C that lie on the same straight line, illustrating the concept of collinearity.
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4 Topics · ICSE Class 9 Mathematics

Topics in Distance Formula

1

1. Distance Formula and Its Meaning

  • The distance formula finds the distance between two points using the differences of their abscissae and ordinates.
  • The formula is derived using Pythagoras' Theorem on a right-angled triangle formed by the two points.
  • In the derivation triangle, AC equals the difference between the abscissae of the two points.
2

2. Solved Distance Problems

  • Distance between (3,6) and (0,2) is 5 units.
  • Distance from the origin to (-12,5) is 13 units.
  • Distance from the origin to (15,-8) is 17 units.
3

3. Collinearity, Triangle Properties, and Special Figures

  • Three points are collinear if and only if the sum of two smaller distances equals the largest distance.
  • For points A(1,-1), B(6,4), and C(4,2), BC + AC = AB, so the points are collinear.
  • Triangle ABC with A(8,3), B(0,9), and C(14,11) is an isosceles right-angled triangle.
4

4. Circumcentre of a Triangle

  • The circumcentre is the point equidistant from the three vertices of a triangle.
  • If P is the circumcentre of triangle ABC, then PA = PB = PC = circumradius.
  • A circle with centre P and radius PA, PB, or PC passes through all three vertices.

Key Concepts

Central concept: Distance formula in coordinate geometry

Two given pointsRight-angled triangle ABCPythagoras' TheoremDistance FormulaDistance from originPoints on axesApplications of distance formulaCollinear points

Frequently Asked Questions

What are the important topics in Distance Formula for ICSE Class 9 Mathematics?
Distance Formula covers several key topics that are frequently asked in ICSE Class 9 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Distance Formula — ICSE Class 9 Mathematics?
Understand the core concepts first, then work through the 33 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

More resources for Distance Formula

All 28 chapters — ICSE Class 9 Mathematics Syllabus

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