Cartesian System of Coordinates
Kerala Board · Class 12 · Mathematics
Summary of Cartesian System of Coordinates for Kerala Board Class 12 Mathematics. Key concepts, important points, and chapter overview.
Overview
The Cartesian System of Coordinates is a fundamental concept in coordinate geometry that bridges the gap between algebra and geometry. Named after René Descartes, this system allows us to represent points in a plane using ordered pairs of numbers, enabling us to solve geometric problems using algebr
Key Concepts
A system consisting of two perpendicular
A system consisting of two perpendicular lines (x-axis and y-axis) intersecting at origin O(0,0), dividing the plane into four quadrants. Any point P
Distance between points P₁(x₁
Distance between points P₁(x₁,y₁) and P₂(x₂,y₂) = √[(x₂-x₁)² + (y₂-y₁)²]. Step-by-step approach: 1) Identify coordinates, 2) Find differences (x₂-x₁)
Internal division
Internal division: Point dividing line segment joining (x₁,y₁) and (x₂,y₂) in ratio m:n is ((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n)). External division: ((mx
Area = ½|x₁(y₂
Area = ½|x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂)| or using determinant form. Step-by-step method: 1) Write coordinates in order, 2) Apply formula systematic
Slope m = tan θ =
Slope m = tan θ = (y₂-y₁)/(x₂-x₁). Parallel lines: m₁ = m₂. Perpendicular lines: m₁ × m₂ = -1. Problem-solving approach: 1) Calculate slopes, 2) Apply
Learning Objectives
- Define and understand the Cartesian coordinate system including origin, axes, and quadrants
- Master the distance formula and apply it to solve problems involving lengths and geometric shapes
- Derive and use section formulas for internal and external division of line segments
- Calculate areas of triangles using coordinate geometry and verify collinearity of points
- Understand slope concepts including inclination, parallelism, and perpendicularity conditions
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What are the important topics in Cartesian System of Coordinates for Kerala Board Class 12 Mathematics?
Cartesian System of Coordinates covers several key topics that are frequently asked in Kerala Board 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 — Kerala Board Class 12 Mathematics?
Start by understanding all key concepts. Practise previous year questions from this chapter. Revise formulas and definitions regularly. Use flashcards for quick revision before the exam.
Sources & Official References
- Kerala Board of Public Examinations — keralapareekshabhavan.in
- National Education Policy 2020 — education.gov.in
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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Differentiation Of Exponential and Logarithmic Functions
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Applications Of Derivatives – Tangents and Normal
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