Cartesian System of Coordinates — Formula Sheet

PQ = √[(x₂ - x₁)² + (y₂ - y₁)²]

OP = √(x² + y²)

((m₁x₂ + m₂x₁)/(m₁ + m₂), (m₁y₂ + m₂y₁)/(m₁ + m₂))

((m₁x₂ - m₂x₁)/(m₁ - m₂), (m₁y₂ - m₂y₁)/(m₁ - m₂))

((x₁ + x₂)/2, (y₁ + y₂)/2)

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

½ |Determinant of [[x₁,y₁,1],[x₂,y₂,1],[x₃,y₃,1]]|

Distance from origin to point P(x, y) is √(x² + y²).

Distance from origin to point (x, y) is √(x² + y²).

The distance between two points P(x₁, y₁) and Q(x₂, y₂) is given by √[(x₂−x₁)² + (y₂−y₁)²].

The slope (m) of a line is the tangent of the angle (θ) it makes with the positive x-axis: m = tanθ.