Coordinate System — Revision Notes
JEE Mains · Mathematics
Quick revision notes for Coordinate System — key concepts, formulas, and definitions for JEE Mains Mathematics preparation.
Revision Notes — Coordinate System
Key concepts, formulas, and definitions from Coordinate System for JEE Mains Mathematics preparation.
Key Topics to Revise
Rectangular Coordinate System and Quadrants
- Two perpendicular axes (x-axis horizontal, y-axis vertical) divide plane into four quadrants
- Point P(x,y): x is abscissa (distance from y-axis), y is ordinate (distance from x-axis)
- Quadrant I: (+,+), II: (-,+), III: (-,-), IV: (+,-)
Transformation of Axes
- Translation of axes: Origin shifted to (h,k), new coordinates X = x-h, Y = y-k
- Rotation of axes: Axes rotated by angle θ about origin
- For rotation: X = x cos θ + y sin θ, Y = -x sin θ + y cos θ
Distance Formula and Applications
- Distance between P(x₁,y₁) and Q(x₂,y₂): d = √[(x₂-x₁)² + (y₂-y₁)²]
- Distance from origin to point (x,y): √(x² + y²)
- For collinear points: distances satisfy triangle inequality as equality
Area of Polygons
- Area of triangle with vertices (x₁,y₁), (x₂,y₂), (x₃,y₃): ½|x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂)|
- Determinant form: Area = ½|determinant of 3×3 matrix|
- For collinear points, area = 0
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Key Concepts
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What topics are covered in Coordinate System for JEE Mains?
Coordinate System is an important chapter in JEE Mains Mathematics. It covers key concepts and formulas that are frequently tested in the exam. Key topics include: Rectangular Coordinate System and Quadrants, Transformation of Axes, Distance Formula and Applications, Area of Polygons.
How important is Coordinate System for JEE Mains?
Coordinate System is a frequently tested chapter in JEE Mains Mathematics. Questions from this chapter appear regularly in previous year papers. There are 57 practice questions available for this chapter.
How to prepare Coordinate System for JEE Mains?
Start by understanding the core concepts, then solve practice questions. Focus on formulas and their applications. Use revision notes for quick review before the exam.