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Cartesian System of Coordinates — Revision Notes

Telangana Open School (TOSS) · Class 12 · Mathematics

Cartesian System of Coordinates revision notes for Telangana Open School (TOSS) Class 12 Mathematics: 4 topics in quick points.

49 questions24 flashcards11 formulas & key relations5 concepts

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Key Topics to Revise

1

1. Cartesian Coordinate System and Quadrants

  • Two perpendicular lines, X'OX (x-axis) and Y'OY (y-axis), intersect at origin O(0,0).
  • Any point P in the plane has coordinates (x, y), where x is the abscissa (horizontal distance) and y is the ordinate (vertical distance).
  • The coordinate axes divide the plane into four quadrants with specific sign conventions.
2

2. Distance Formula

  • Distance between two points P(x₁, y₁) and Q(x₂, y₂) is calculated using the Pythagorean theorem.
  • The formula works for all quadrants.
  • Distance from origin to point P(x, y) is √(x² + y²).
3

3. Section Formula and Midpoint

  • Section formula finds coordinates of a point dividing a line segment in a given ratio.
  • Internal division: R divides PQ in ratio m₁:m₂ → coordinates are weighted averages.
  • External division: point lies outside the segment.
4

4. Area of a Triangle

  • Area of triangle with vertices (x₁,y₁), (x₂,y₂), (x₃,y₃) can be found using determinant method.
  • Take absolute value of half the determinant to get positive area.
  • If area is zero, the three points are collinear.

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Full Notes

Key Concepts

The Cartesian plane consists of twoThe distance between two points P(x₁If a point R dividesThe area of a triangleThe slope (m) of a line

Frequently Asked Questions

What are the important topics in Cartesian System of Coordinates for Telangana Open School (TOSS) Class 12 Mathematics?
Key topics in Cartesian System of Coordinates include Cartesian Coordinate System and Quadrants, Distance Formula, Section Formula and Midpoint, Area of a Triangle. Study these first, then practise questions on each for the Telangana Open School (TOSS) Class 12 board exam.
How should I revise Cartesian System of Coordinates for the Telangana Open School (TOSS) Class 12 board exam?
Learn the core ideas first, then work through the 49 practice questions on Cartesian System of Coordinates. 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 Telangana Open School (TOSS) Class 12 Mathematics Revision Notes

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