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Coordinate Geometry Calculator

Comprehensive coordinate geometry tools: calculate distance between points, midpoint, section formula, slope, area of triangle, equation of line, and more.

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Distance Calculator

Calculate distance between two points, point to line, or between parallel lines in 2D coordinate geometry.

Midpoint Calculator

Find midpoint, endpoint, or trisection points of a line segment given coordinates.

Section Formula Calculator

Find point dividing line segment in given ratio (internal or external division).

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Slope & Line Equation

Calculate slope, angle, and find equation of line in various forms.

Area of Triangle (Coordinates)

Calculate area of triangle using coordinates of vertices, determinant method, or distance formula.

Triangle Centers

Calculate centroid, circumcenter, orthocenter, and incenter of triangle from coordinates.

Coordinate Geometry Formulas Reference

Quick reference for all coordinate geometry formulas used in this calculator.

Distance Formulas

Between Two Points
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
Point to Line
d = |Ax₀ + By₀ + C| / √(A² + B²)
Parallel Lines
d = |C₂ - C₁| / √(A² + B²)

Midpoint & Section

Midpoint Formula
M = ((x₁+x₂)/2, (y₁+y₂)/2)
Internal Division
P = ((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n))
External Division
P = ((mx₂-nx₁)/(m-n), (my₂-ny₁)/(m-n))

Slope & Line Equations

Slope Formula
m = (y₂ - y₁)/(x₂ - x₁)
Angle to Slope
m = tan(θ)
Line Equation Forms
y - y₁ = m(x - x₁)
y = mx + c, Ax + By + C = 0

Area & Triangle Centers

Area (Determinant)
Area = ½|x₁(y₂-y₃)+x₂(y₃-y₁)+x₃(y₁-y₂)|
Centroid
G = ((x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3)
Collinearity Check
x₁(y₂-y₃)+x₂(y₃-y₁)+x₃(y₁-y₂) = 0