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  "body": "\n## Definition\n\nLet $K$ be a field in which $2 \\neq 0$, and let $A$ be an [[affine space|09XNAPTJQ7]] over a vector space $V$ over $K$. Let $p$ and $q$ be points of $A$.\nThe midpoint of $p$ and $q$ is the point\n$$\\operatorname{midpoint}(p, q) = p + \\tfrac{1}{2}(q - p).$$\nIt is the [[affine combination|0KJH6SRFZK]] $\\frac{1}{2} p + \\frac{1}{2} q$.\n\n## Remarks\n\nIn $\\mathbb{R}^n$, the midpoint of $(p_1, \\dots, p_n)$ and $(q_1, \\dots, q_n)$ is $\\left(\\frac{p_1 + q_1}{2}, \\dots, \\frac{p_n + q_n}{2}\\right)$.\nIn a Euclidean space, the midpoint $m$ of $p$ and $q$ satisfies $d(p, m) = d(m, q) = \\frac{1}{2} d(p, q)$. It is the only point with this property.\nThe midpoint is symmetric: $\\operatorname{midpoint}(p, q) = \\operatorname{midpoint}(q, p)$. Also $\\operatorname{midpoint}(p, p) = p$.\n\n## Explanations\n\n### L1 human\n\nThe midpoint is the average of the two points. To find it, take the average of each coordinate. For example, the midpoint of $(0, 0)$ and $(4, 6)$ is $(2, 3)$.\n",
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