Geometry
Coordinate geometry
Distances, midpoints, slopes and areas from coordinates.
Geometry
Distance between two points
d = √((x₂−x₁)² + (y₂−y₁)²)→GeometryMidpoint x-coordinate
xₘ = (x₁ + x₂) / 2→GeometryLine slope
k = (y₂−y₁) / (x₂−x₁)→GeometryTriangle area from coordinates
S = ½|x₁(y₂−y₃)+x₂(y₃−y₁)+x₃(y₁−y₂)|→GeometrySimilarity ratio from sides
k = a₁ / a₂→GeometrySimilarity ratio from perimeters
k = P₁ / P₂→GeometrySimilarity ratio from areas
k = √(S₁ / S₂)→GeometrySimilarity ratio of linear elements
k = l₁ / l₂→GeometryFourth term of a similar-triangle proportion
a₁/a₂ = b₁/b₂; a₁ = a₂b₁/b₂→GeometrySimilar triangle side from ratio
a₂ = a₁ / k→GeometryTriangle perimeter from coordinates
P = d₁₂ + d₂₃ + d₃₁→GeometryTriangle existence by sides
a+b>c, a+c>b, b+c>a→GeometryTriangle type by sides and angles
Triangle type by sides and angles: calculated from the entered values→GeometryAngle between two vectors in 2D
α = acos((u·v)/(|u||v|))→GeometrySegment midpoint coordinates
M((x₁+x₂)/2, (y₁+y₂)/2)→GeometryLine equation through two points
Ax + By + C = 0→GeometryPoint-to-line distance
d = |Ax₀+By₀+C|/√(A²+B²)→GeometryAngle between two lines
φ = atan(|A₁B₂−A₂B₁|/|A₁A₂+B₁B₂|)→GeometryIntersection point of two lines
A₁x+B₁y+C₁=0; A₂x+B₂y+C₂=0→