Coordinate geometry

Distance

d = √[(x₂ − x₁)² + (y₂ − y₁)²]

Section formula

((mx₂ + nx₁)/(m + n), (my₂ + ny₁)/(m + n))

Internal division in m : n

Midpoint

((x₁ + x₂)/2, (y₁ + y₂)/2)

Slope

m = (y₂ − y₁)/(x₂ − x₁)

Parallel: m₁ = m₂; perpendicular: m₁m₂ = −1

Triangle area

½|x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)|

Zero ⇒ points collinear

Point to line distance

|ax₁ + by₁ + c| / √(a² + b²)

Circle equation

(x − h)² + (y − k)² = r²

Centre (h, k)