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Cartesian System of Coordinates — Syllabus

Telangana Open School (TOSS) · Class 12 · Mathematics

What Cartesian System of Coordinates covers in Telangana Open School (TOSS) Class 12 Mathematics: 4 topics, for the 2026-27 session.

49 questions24 flashcards11 formulas & key relations5 concepts

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4 Topics · Telangana Open School (TOSS) Class 12 Mathematics · 2026-27

Topics in Cartesian System of Coordinates

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.

Key Concepts

Central concept: Cartesian System of Coordinates

Coordinate AxesCoordinates of a PointDistance FormulaSection FormulaArea of a TriangleSlope of a LineIntercepts of a LineLocus of a Point

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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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