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Coordinate Geometry — Revision Notes

Tamil Nadu Board · Class 9 · Mathematics

Coordinate Geometry revision notes for Tamil Nadu Board Class 9 Mathematics: 4 topics in quick points. Includes The Cartesian Coordinate System, Distance.

45 questions25 flashcards5 formulas & key relations5 concepts

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A labeled diagram showing the x-axis, y-axis, origin, and a point (x, y) in the first quadrant, illustrating the basic setup of a Cartesian coordinate system.
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Key Topics to Revise

1

The Cartesian Coordinate System

  • The Cartesian plane is formed by two number lines – the horizontal x-axis and the vertical y-axis – intersecting at right angles at a point called the Origin O(0,0).
  • Every point on the plane is represented by an ordered pair (x, y), where x is called the abscissa (x-coordinate) and y is called the ordinate (y-coordinate).
  • The order matters: (x, y) ≠ (y, x) unless x = y.
2

Distance Formula

  • The distance between two points P(x₁, y₁) and Q(x₂, y₂) is derived using the Pythagoras theorem.
  • A right triangle PQR is formed where PR is horizontal and RQ is vertical.
  • PR = |x₂ − x₁| and RQ = |y₂ − y₁|.
3

Mid-Point Formula

  • The mid-point M of a line segment joining A(x₁, y₁) and B(x₂, y₂) is the average of the coordinates.
  • The x-coordinate of M = average of x-coordinates = (x₁ + x₂)/2.
  • The y-coordinate of M = average of y-coordinates = (y₁ + y₂)/2.
4

Section Formula

  • The section formula gives the coordinates of a point P that divides the line segment joining A(x₁,y₁) and B(x₂,y₂) internally in the ratio m:n.
  • The formula is derived using similar triangles.
  • When m = n = 1, the section formula reduces to the mid-point formula.

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Full Notes

Key Concepts

A coordinate system consists of twoTo plot a point (xThe distance d between two pointsThe midpoint M of a lineWhen a point P divides

Frequently Asked Questions

What are the important topics in Coordinate Geometry for Tamil Nadu Board Class 9 Mathematics?
Key topics in Coordinate Geometry include The Cartesian Coordinate System, Distance Formula, Mid-Point Formula, Section Formula. Study these first, then practise questions on each for Class 9 exams.
How should I revise Coordinate Geometry for Class 9 exams?
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 9 Mathematics Revision Notes

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