Lesson 4.6: Coordinate Geometry
Coordinate Geometry is an important part of the Mathematics section for NDA, CDS, and AFCAT exams. It helps aspirants solve problems related to points, lines, distance, and slope in the 2D plane.
1. Basics of Coordinate Geometry
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Coordinate Plane: Consists of X-axis (horizontal) and Y-axis (vertical)
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Coordinates: A point P represented as (x, y)
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Quadrants: Four quadrants dividing the plane
2. Distance Formula
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Distance between two points P(x₁, y₁) and Q(x₂, y₂):
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Distance=(x2−x1)2+(y2−y1)2\text{Distance} = \sqrt{(x₂-x₁)² + (y₂-y₁)²}
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3. Midpoint Formula
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Midpoint of line joining P(x₁, y₁) and Q(x₂, y₂):
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Midpoint=(x1+x22,y1+y22)\text{Midpoint} = \left(\frac{x₁+x₂}{2}, \frac{y₁+y₂}{2}\right)
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4. Slope of a Line
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Slope (m) = (y₂ – y₁) / (x₂ – x₁)
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Interpretation:
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m > 0 → Line rises
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m < 0 → Line falls
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m = 0 → Horizontal line
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Undefined → Vertical line
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5. Equation of a Line
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Slope-Intercept Form: y = mx + c
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Point-Slope Form: y – y₁ = m(x – x₁)
Exam Tips
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Memorize distance, midpoint, and slope formulas.
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Practice line equations and simple graph plotting.
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Solve previous year NDA, CDS, AFCAT coordinate geometry questions.
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Focus on accuracy and diagram visualization.