Collinearity

Collinearity is the property of points lying on one straight line. In a plane, any two distinct points determine a unique line, so collinearity is informative for sets of at least three points.

Point (geometry): A point is an exact location with no size or extension. Collinearity asks whether several geometric locations belong to one line.
Collinearity criterion: A collinearity criterion is a condition equivalent to a set of points lying on one line. Coordinate and area criteria provide practical tests for the defining property.
Menelaus's theorem: Menelaus's theorem relates the directed ratios formed when a transversal intersects the three sides of a triangle. Its converse determines whether three side-intersection points are collinear.
Concurrency (geometry): Concurrency is the property of several lines passing through one common point. It is the dual-looking incidence relation: lines meet at a point rather than points sharing a line.
Straight line: A straight line is a one-dimensional geometric object extending infinitely in both directions. It is the shared geometric object that collinear points lie on.
Area of a triangle: The area of a triangle is half the product of a base and its corresponding height. Three points are collinear exactly when their triangle has zero area.
Pascal's theorem: Pascal's theorem states that opposite-side intersections of a hexagon inscribed in a conic lie on one line. The theorem produces a notable collinear triple from six points on a conic.
Coplanarity: Coplanarity is the property of points or other geometric objects lying in one plane. In three dimensions, collinearity implies coplanarity, but coplanarity alone does not imply collinearity.
Coordinate geometry: Coordinate geometry describes geometric objects and relationships using numbers and algebra. Coordinates turn collinearity into equations that can be checked algebraically.
Linear dependence: A set of vectors is linearly dependent when a nontrivial weighted sum of them equals zero. Position vectors relative to a fixed point are dependent when their endpoints lie on one line through it.

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