Analytic geometry
Lines and planes
Line and plane equations, slopes, intercepts and normals.
Analytic geometry
Line slope from two points
k = (y₂−y₁)/(x₂−x₁)→Analytic geometryLine y-value
y = kx+b→Analytic geometryLine x-intercept
x₀ = −C/A→Analytic geometryLine y-intercept
y₀ = −C/B→Analytic geometryPlane z-coordinate
z = −(Ax+By+D)/C→Analytic geometryPlane normal magnitude
|n| = √(A²+B²+C²)→Analytic geometryLine through two points
Ax + By + C = 0→Analytic geometryPlane through three points
Ax + By + Cz + D = 0→Analytic geometryPoint-plane distance from three points
d = |Ax₀+By₀+Cz₀+D|/|n|→Analytic geometrySegment division in a ratio
M = (nA + mB)/(m+n)→Analytic geometryPoint projection on a line
H = A + t(B−A)→Analytic geometryParallel-lines distance from points
d(L₁,L₂)→Analytic geometryCircle tangent at a point
(P−O)·(X−P)=0→