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Distance Formula — Revision Notes

ICSE · Class 9 · Mathematics

Distance Formula revision notes for ICSE Class 9 Mathematics: 4 topics in quick points. Part of the ICSE Class 9 Mathematics syllabus.

33 questions24 flashcards7 formulas & key relations5 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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Key Topics to Revise

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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.
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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.
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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.
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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.

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Key Concepts

For points A(x1A rightThe distance of any point (xA point on the xThree points

Frequently Asked Questions

What are the important topics in Distance Formula for ICSE Class 9 Mathematics?
Key topics in Distance Formula include Distance Formula and Its Meaning, Solved Distance Problems, Collinearity, Triangle Properties, and Special Figures, Circumcentre of a Triangle. Study these first, then practise questions on each for Class 9 exams.
How should I revise Distance Formula for Class 9 exams?
Learn the core ideas first, then work through the 33 practice questions on Distance Formula. Revise 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.

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All ICSE Class 9 Mathematics Revision Notes

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