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距离公式

逐步推导得出两点间距离的一般公式。
left parenthesis, start color #1fab54, x, start subscript, 1, end subscript, end color #1fab54, comma, start color #e07d10, y, start subscript, 1, end subscript, end color #e07d10, right parenthesisleft parenthesis, start color #1fab54, x, start subscript, 2, end subscript, end color #1fab54, comma, start color #e07d10, y, start subscript, 2, end subscript, end color #e07d10, right parenthesis 两点之间的 start color #11accd, start text, 距, 离, end text, end color #11accd 用下面的公式表示:
square root of, left parenthesis, start color #1fab54, x, start subscript, 2, end subscript, minus, x, start subscript, 1, end subscript, end color #1fab54, right parenthesis, squared, plus, start color #e07d10, left parenthesis, y, start subscript, 2, end subscript, minus, y, start subscript, 1, end subscript, end color #e07d10, right parenthesis, squared, end square root
在本文中, 我们将推导这个公式!

推导距离公式

让我们开始绘制点 left parenthesis, start color #1fab54, x, start subscript, 1, end subscript, end color #1fab54, comma, start color #e07d10, y, start subscript, 1, end subscript, end color #e07d10, right parenthesis 和点 left parenthesis, start color #1fab54, x, start subscript, 2, end subscript, end color #1fab54, comma, start color #e07d10, y, start subscript, 2, end subscript, end color #e07d10, right parenthesis.
两点之间线段的长度即为它们之间的 start color #11accd, start text, 距, 离, end text, end color #11accd:
我们需要求出这段 start color #11accd, start text, 距, 离, end text, end color #11accd. 如果我们画一个直角三角形, 我们就可以用勾股定理!
底边长度的表达为 start color #1fab54, x, start subscript, 2, end subscript, minus, x, start subscript, 1, end subscript, end color #1fab54:
同样地, 高的长度表达为 start color #e07d10, y, start subscript, 2, end subscript, minus, y, start subscript, 1, end subscript, end color #e07d10:
现在我们可以使用勾股定理写下方程式:
start color #11accd, question mark, end color #11accd, squared, equals, left parenthesis, start color #1fab54, x, start subscript, 2, end subscript, minus, x, start subscript, 1, end subscript, end color #1fab54, right parenthesis, squared, plus, start color #e07d10, left parenthesis, y, start subscript, 2, end subscript, minus, y, start subscript, 1, end subscript, end color #e07d10, right parenthesis, squared
我们可以通过取两边的平方根来求出 start color #11accd, question mark, end color #11accd :
start color #11accd, question mark, end color #11accd, equals, square root of, left parenthesis, start color #1fab54, x, start subscript, 2, end subscript, minus, x, start subscript, 1, end subscript, end color #1fab54, right parenthesis, squared, plus, start color #e07d10, left parenthesis, y, start subscript, 2, end subscript, minus, y, start subscript, 1, end subscript, end color #e07d10, right parenthesis, squared, end square root
就是这样! 我们得到了距离公式!
有趣的是, 很多人实际并不记得这个公式. 相反, 他们会建立一个直角三角形, 任何时候他们想要求两点之间的距离时,就用勾股定理.

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