中点公式

$(\greenD{x_1}, \goldD{y_1})$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$(\greenD{x_2}, \goldD{y_2})$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的$\blueD{\text{中点}}$start color #11accd, start text, 中, 点, end text, end color #11accd，通过已知公式 :

在本文中, 我们将推导这个公式!

让我们开始绘制点 $(\greenD{x_1}, \goldD{y_1})$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 $(\greenD{x_2}, \goldD{y_2})$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.

$\blueD{\text{中点}}$start color #11accd, start text, 中, 点, end text, end color #11accd 为每个点中间的点:

$x$x-坐标的 $\blueD{\text{中点}}$start color #11accd, start text, 中, 点, end text, end color #11accd 表达式是 $\greenD{\dfrac{x_1+x_2}{2}}$start color #1fab54, start fraction, x, start subscript, 1, end subscript, plus, x, start subscript, 2, end subscript, divided by, 2, end fraction, end color #1fab54:

相似, $y$y-坐标的 $\blueD{\text{中点}}$start color #11accd, start text, 中, 点, end text, end color #11accd 表达式是 $\goldD{\goldD{\dfrac{y_1+y_2}{2}}}$start color #e07d10, start color #e07d10, start fraction, y, start subscript, 1, end subscript, plus, y, start subscript, 2, end subscript, divided by, 2, end fraction, end color #e07d10, end color #e07d10:

就这样! 我们推导出了 $\blueD{\text{中点}}$start color #11accd, start text, 中, 点, end text, end color #11accd的公式!

有趣的是, 很多人都记不住这个准确的公式. 反而, 他们记得为了找到中点, 必须取 $x$x-坐标的平均值和$y$y-坐标的平均值.