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Key Concepts
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1. Cartesian System
A plane is divided into four quadrants by two perpendicular axes (X-axis and Y-axis). The intersection point is the Origin (0,0).
2. Distance Formula
The distance between two points P(x₁, y₁) and Q(x₂, y₂) is given by:
PQ = √[(x₂ - x₁)² + (y₂ - y₁)²]
3. Section Formula
The coordinates of point P which divides the line segment joining A(x₁, y₁) and B(x₂, y₂) in ratio m₁:m₂ are:
x = (m₁x₂ + m₂x₁) / (m₁ + m₂), y = (m₁y₂ + m₂y₁) / (m₁ + m₂)
- Midpoint: ((x₁+x₂)/2, (y₁+y₂)/2)
4. Area of a Triangle
Area = |½[x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂)]|