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Coordinate Geometry — Revision Notes

Tamil Nadu Board · Class 10 · Mathematics

Coordinate Geometry revision notes for Tamil Nadu Board Class 10 Mathematics: 4 topics in quick points. Includes Area of Triangle Using Coordinates.

45 questions25 flashcards11 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

1

1. Area of Triangle Using Coordinates

  • Area formula when three vertices are known: Area = ½|{(x₁y₂ + x₂y₃ + x₃y₁) - (x₂y₁ + x₃y₂ + x₁y₃)}|
  • Vertices must be taken in counter-clockwise order to avoid negative areas
  • Three collinear points always form a triangle with area = 0
2

2. Collinearity Test Using Slope and Area

  • Method 1: Three points are collinear if area of triangle = 0
  • Method 2: Three points A(x₁,y₁), B(x₂,y₂), C(x₃,y₃) are collinear if x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂) = 0
  • Method 3: Points are collinear if slope of AB = slope of BC = slope of AC
3

3. Area of Quadrilateral Using Coordinates

  • Quadrilateral area = Area of △1 + Area of △2 (divide using diagonal)
  • Standard formula: Area = ½|{(x₁y₂ + x₂y₃ + x₃y₄ + x₄y₁) - (x₂y₁ + x₃y₂ + x₄y₃ + x₁y₄)}|
  • Take vertices in counter-clockwise order for consistency
4

4. Slope of a Line and Its Properties

  • Slope m = tan(θ) where θ is angle with positive x-axis (inclination)
  • Slope formula: m = (y₂-y₁)/(x₂-x₁) for points (x₁,y₁) and (x₂,y₂)
  • Slope = 0 for horizontal lines (parallel to x-axis)

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Full Notes

Key Concepts

The distance between two points A(x₁For a triangle with vertices atThree distinct points A(x₁For a quadrilateral with vertices A(x₁The slope (gradient) m of

Frequently Asked Questions

What are the important topics in Coordinate Geometry for Tamil Nadu Board Class 10 Mathematics?
Key topics in Coordinate Geometry include Area of Triangle Using Coordinates, Collinearity Test Using Slope and Area, Area of Quadrilateral Using Coordinates, Slope of a Line and Its Properties. Study these first, then practise questions on each for the Tamil Nadu Board Class 10 board exam.
How should I revise Coordinate Geometry for the Tamil Nadu Board Class 10 board exam?
Learn the core ideas first, then work through the 45 practice questions on Coordinate Geometry. 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.

More resources for Coordinate Geometry

All Tamil Nadu Board Class 10 Mathematics Revision Notes

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