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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

  1. For the hyperbola x²/a² - y²/b² = 1, the asymptotes are:

    • y = ±ax/b
    • y = ±(b/a)x
    • y = ±a
    • y = ±b
    Show answer

    Answer: y = ±(b/a)x

  2. Number of points common to a line and a circle can be:

    • Always 2
    • 0 or 2 only
    • 0, 1, or 2
    • Always 1
    Show answer

    Answer: 0, 1, or 2

  3. The equation y² = x represents a:

    • Circle
    • Ellipse
    • Parabola with axis along x-axis
    • Hyperbola
    Show answer

    Answer: Parabola with axis along x-axis

  4. The equation 3x - 4y + 12 = 0 has x-intercept:

    • -4
    • -3
    • 3
    • 4
    Show answer

    Answer: -4

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Practice Questions

Practise PRMO questions on Coordinate Geometry. Answers are revealed after each question.

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Geometry