Coordinate Geometry
Distance, midpoint, slopes, conic sections, and loci
Key Concepts
- Distance and section formulas locate points
- The shoelace formula gives a polygon's area from its vertices
- Lines and circles have standard coordinate equations
- Collinearity and concurrency can be tested algebraically
Important Formulae
| Distance | √((x₂−x₁)² + (y₂−y₁)²) |
| Triangle area (shoelace) | ½ |x₁(y₂−y₃) + x₂(y₃−y₁) + x₃(y₁−y₂)| |
| Section formula | ((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n)) |
Quick Tips
- Three points are collinear if the triangle area they form is zero.
- Placing the figure with a convenient origin simplifies the algebra.
Sample Practice Questions
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The locus of points equidistant from (2,0) and (-2,0) is:
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Answer: The y-axis (x = 0)
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A circle passes through (1,0), (-1,0), (0,1). Its centre is:
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Answer: (0, 0)
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How many lattice points (integer coordinates) are inside the circle x² + y² = 5?
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Answer: 9
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Three points A, B, C are collinear when the area of triangle ABC is:
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Answer: 0
Practice Questions
Practise PRMO questions on Coordinate Geometry. Answers are revealed after each question.
Start Practice →Frequently Asked Questions
What are the key concepts in Coordinate Geometry for PRMO?
Distance and section formulas locate points; The shoelace formula gives a polygon's area from its vertices; Lines and circles have standard coordinate equations; Collinearity and concurrency can be tested algebraically.
Which formulae are important for Coordinate Geometry in PRMO?
Distance: √((x₂−x₁)² + (y₂−y₁)²); Triangle area (shoelace): ½ |x₁(y₂−y₃) + x₂(y₃−y₁) + x₃(y₁−y₂)|; Section formula: ((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n)).
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