Coordinate Geometry — Formula Sheet

Area formula when three vertices are known

Area = ½|{(x₁y₂ + x₂y₃ + x₃y₁) - (x₂y₁ + x₃y₂ + x₁y₃)}|

Three collinear points always form a triangle with area = 0

Method 1

Three points are collinear if area of triangle = 0

Method 2

Three points A(x₁,y₁), B(x₂,y₂), C(x₃,y₃) are collinear if x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂) = 0

Method 3

Points are collinear if slope of AB = slope of BC = slope of AC

Quadrilateral area = Area of △1 + Area of △2 (divide using diagonal)

Slope m = tan(θ) where θ is angle with positive x-axis (inclination)

Slope formula

m = (y₂-y₁)/(x₂-x₁) for points (x₁,y₁) and (x₂,y₂)

Slope = 0 for horizontal lines (parallel to x-axis)

The distance between two points A(x₁, y₁) and B(x₂, y₂) is calculated using the formula: d = √[(x₂ - x₁)² + (y₂ - y₁)²].

For a line making angle θ with the positive x-axis, slope m = tan(θ).