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Cartesian System of Coordinates

Telangana Open School (TOSS) · Class 12 · Mathematics

Complete topic list for Cartesian System of Coordinates in Telangana Open School (TOSS) Class 12 Mathematics. Key concepts, sub-topics, and what to focus on for board exams.

49 questions24 flashcards5 concepts

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

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

Frequently Asked Questions

What are the important topics in Cartesian System of Coordinates for Telangana Open School (TOSS) Class 12 Mathematics?
Cartesian System of Coordinates covers several key topics that are frequently asked in Telangana Open School (TOSS) Class 12 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Cartesian System of Coordinates — Telangana Open School (TOSS) Class 12 Mathematics?
Understand the core concepts first, then work through the 49 practice questions available for this chapter. Revise formulas and 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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