Coordinate Geometry

The distance between two points A(x₁

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

For a triangle with vertices at

For a triangle with vertices at A(x₁, y₁), B(x₂, y₂), and C(x₃, y₃), the area is: Area = ½|{(x₁y₂ + x₂y₃ + x₃y₁) - (x₂y₁ + x₃y₂ + x₁y₃)}| square units

Three distinct points A(x₁

Three distinct points A(x₁, y₁), B(x₂, y₂), and C(x₃, y₃) are collinear (lie on the same line) if and only if the area of the triangle they form equal

For a quadrilateral with vertices A(x₁

For a quadrilateral with vertices A(x₁, y₁), B(x₂, y₂), C(x₃, y₃), and D(x₄, y₄) taken in order, the area is: Area = ½|{(x₁y₂ + x₂y₃ + x₃y₄ + x₄y₁) -

The slope (gradient) m of

The slope (gradient) m of a line is the measure of its steepness and direction. For a line making angle θ with the positive x-axis, slope m = tan(θ).