Ocegik / Coordinate Geometry
Coordinate Geometry Formulas for CAT Preparation
Revise coordinate geometry formulas from Ocegik’s formula library, with named identities, expressions and usage notes grouped by topic.
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Coordinate Geometry: formulas by topic
FundamentalsCoordinate Geometry
Distance formula√((x2 − x1)2 + (y2 − y1)2)between points (x₁,y₁) and (x₂,y₂)
Area of a triangle (vertices)12|x1(y2−y3) + x2(y3−y1) + x3(y1−y2)|(x₁,y₁), (x₂,y₂), (x₃,y₃) are the triangle's vertices
Section formula (internal/external)(mx2 ± nx1m ± n, my2 ± ny1m ± n)point dividing (x₁,y₁)–(x₂,y₂) in the ratio m:n; + for internal, − for external division
Mid-point(x1+x22, y1+y22)
Centroid of a triangle(x1+x2+x33, y1+y2+y33)
Slope of a linem = y2 − y1x2 − x1
Parallel linesm1 = m2
Perpendicular linesm1m2 = −1
Equations of a LineCoordinate Geometry
Slope–intercept formy = mx + c
Point–slope formy − y1 = m(x − x1)
Two-point formy − y1 = y2 − y1x2 − x1(x − x1)
Length of perpendicular from a pointp = |ax1 + by1 + c| / √(a2 + b2)from point (x₁,y₁) to the line ax + by + c = 0
Perpendicular distance from origin= |c| / √(a2 + b2)
Distance between two parallel lines= |c2 − c1| / √(a2 + b2)lines ax + by + c₁ = 0 and ax + by + c₂ = 0
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