Coordinate Geometry

The distance between two points A(x₁

The distance between two points A(x₁, y₁) and B(x₂, y₂) is given by d = √[(x₂-x₁)² + (y₂-y₁)²]. For points on axes: distance between points on X-axis

If point P divides line segment

If point P divides line segment AB joining A(x₁, y₁) and B(x₂, y₂) in ratio m₁:m₂, then P = [(m₁x₂ + m₂x₁)/(m₁ + m₂), (m₁y₂ + m₂y₁)/(m₁ + m₂)]. For mi

The centroid is the point where

The centroid is the point where all three medians of a triangle intersect. For triangle with vertices A(x₁, y₁), B(x₂, y₂), C(x₃, y₃), centroid = [(x₁

Area = ½|x₁(y₂

Area = ½|x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂)| using coordinates. Also calculated using Heron's formula: Area = √[s(s-a)(s-b)(s-c)] where s = (a+b+c)/2.

Slope of line passing through points

Slope of line passing through points (x₁, y₁) and (x₂, y₂) is m = (y₂-y₁)/(x₂-x₁). Slope represents the rate of change and angle of inclination with X