Quick Review: Coordinate Geometry

Important Formulas

• Distance PQ =


• Slope of PQ = m =


• Equation of or y = mx + c
• The product of the slopes of two perpendicular lines is –1.
• The distance between the points (x₁, y₁) and (x₂, y₂) is


• If point P(x, y) divides the segment AB, where A ≡ (x₁, y₁) and B ≡ (x₂, y₂), internally in the ratio m: n, then,
  x= (mx₂ + nx₁)/(m+n)
  and
  y= (my₂ + ny₁)/(m+n)
• If P is the midpoint then,


• If G (x, y) is the centroid of triangle ABC, A ≡ (x₁, y₁), B ≡ (x₂, y₂), C ≡ (x₃, y₃), then,
  x = (x₁ + x₂ + x₃)/3 and y = (y₁ + y₂ + y₃)/3


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• If I (x, y) is the in-centre of triangle ABC, A ≡ (x₁, y₁), B ≡ (x₂, y₂), C ≡ (x₃, y₃), then, where a, b and c are the lengths of the BC, AC and AB respectively.
• The equation of a straight line is y = mx + c, where m is the slope and c is the y-intercept (tan θ = m, where θ is the angle that the line makes with the positive X-axis).