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  "body": "\n## Definition\n\nLet $K$ be a field and let $A$ be an [[affine space|09XNAPTJQ7]] over a vector space $V$ over $K$.\nA set $S$ of points of $A$ is collinear if the linear span of the vectors $q - p$ for $p, q \\in S$ has dimension at most 1.\nEquivalently, $S$ is collinear if $S$ has at most one point or a [[line|0MP9BCF6DP]] of $A$ contains $S$.\n\n## Remarks\n\nThe empty set and each set with one point are collinear. Each set of two points is collinear.\nA set $S$ with at least two points is collinear if and only if its [[affine span|0YMB1676R1]] is a line.\nIn $\\mathbb{R}^2$, the points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ are collinear if and only if $(x_2 - x_1)(y_3 - y_1) - (x_3 - x_1)(y_2 - y_1) = 0$.\nMathlib's `Collinear` uses the first form of the definition.\n\n## Explanations\n\n### L1 human\n\nPoints are collinear if you can draw one straight line through all of them. The points $(0, 0)$, $(1, 2)$ and $(2, 4)$ are collinear: they all lie on $y = 2x$. The point $(1, 1)$ is not on this line, so $(0, 0)$, $(1, 2)$ and $(1, 1)$ are not collinear.\n",
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