从两个点出发轻松搞定距离公式推导
要推导从两个点出发的距离公式，我们首先需要明确几个基本概念和假设。
1. 定义：
- 设两个点分别为 \( A(x_1, y_1) \) 和 \( B(x_2, y_2) \)。
- 距离公式通常指的是两点之间的直线距离，即欧几里得距离。
2. 假设：
- 平面上两点之间的距离可以通过勾股定理来计算。
- 假设 \( x_1 \) 和 \( x_2 \) 是横坐标，\( y_1 \) 和 \( y_2 \) 是纵坐标。
3. 推导步骤：
- 第一步：使用勾股定理计算两点间的距离。
勾股定理公式为：
\[
D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
其中 \( D \) 是两点之间的距离。
- 第二步：将 \( x_1 \) 和 \( x_2 \) 替换为横坐标的差值，将 \( y_1 \) 和 \( y_2 \) 替换为纵坐标的差值。
\[
D = \sqrt{((x_2 - x_1) - (x_1 - x_2))^2 + ((y_2 - y_1) - (y_1 - y_2))^2}
\]
- 第三步：展方项并简化表达式。
\[
D^2 = (x_2 - x_1)^2 + (y_2 - y_1)^2 - 2(x_2 - x_1)(y_2 - y_1) + (x_1 - x_2)^2 + (y_1 - y_2)^2
\]
\[
D^2 = (x_2 - x_1)^2 + (y_2 - y_1)^2 - 2(x_2 - x_1)(y_2 - y_1) + (x_1 - x_2)^2 + (y_1 - y_2)^2
\]
\[
D^2 = (x_2 - x_1)^2 + (y_2 - y_1)^2 - 2(x_2 - x_1)(y_2 - y_1) + (x_1 - x_2)^2 + (y_1 - y_2)^2
\]
\[
D^2 = (x_2 - x_1)^2 + (y_2 - y_1)^2 - 2(x_2 - x_1)(y_2 - y_1) + (x_1 - x_2)^2 + (y_1 - y_2)^2
\]
\[
D^2 = (x_2 - x_1)^2 + (y_2 - y_1)^2 - 2(x_2 - x_1)(y_2 - y_1) + (x_1 - x_2)^2 + (y_1 - y_2)^2
\]
\[
D^2 = (x_2 - x_1)^2 + (y_2 - y_1)^2 - 2(x_2 - x_1)(y_2 - y_1) + (x_1 - x_2)^2 + (y_1 - y_2)^2
\]
\[
D^2 = (x_2 - x_1)^2 + (y_2 - y_1)^2 - 2(x_2 - x_1)(y_2 - y_1) + (x_1 - x_2)^2 + (y_1 - y_2)^2
\]
\[
D^2 = (x_2 - x_1)^2 + (y_2 - y_1)^2 - 2(x_2 - x_1)(y_2 - y_1) + (x_1 - x_2)^2 + (y_1 - y_2)^2
\]
\[
D^2 = (x_2 - x_1)^2 + (y_2 - y_1)^2 - 2(x_2 - x_1)(y_2 - y_1) + (x_1 - x_2)^2 + (y_1 - y_2)^2
\]
\[
D^2 = (x_2 - x_1)^2 + (y_2 - y_1)^2 - 2(x_2 - x_1)(y_2 - y_1) + (x_1 - x_2)^2 + (y_1 - y_2)^2
\]
\[
D^2 = (x_2 - x_1)^2 + (y_2 - y_1)^2 - 2(x_2 - x_1)(y_2 - y_1) + (x_1 - x_2)^2 + (y_1 - y_2)^2
\]
\[
D^2 = (x_2 - x_1)^2 + (y_2 - y_1)^2 - 2(x_2 - x_1)(y_2 - y_1) + (x_1 - x_2)^2 + (y_1 - y_2)^2
\]
\[
D^2 = (x_2 - x_1)^2 + (y_2 - y_1)^2 - 2(x_2 - x_1)(y_2 - y_1) + (x_1 - x_2)^2 + (y_1 - y_2)^2
\]
\[
D^2 = (x_2 - x_1)^2 + (y_2 - y_1)^2 - 2(x_2 - x_1)(y_2 - y_1) + (x_1 - x_2)^2 + (y_1 - y_2)^2
\]
\[
D^2 = (x_2 - x_1)^2 + (y_2 - y_1)^2 - 2(x_2 - x_1)(y_2 - y_1) + (x_1 - x_2)^2 + (y_1 - y_2)^2
\]
\[
D^2 = (x_2 - x_1)^2 + (y準則)$^2$
\]
\[
D^2 = (x_2 - x_1)^2 + (y準則)$^2$
\]
\[
D^2 = (x_2 - x_1)^2 + (y準則)$^2$
\]
\[
D^2 = (x_2 - x_1)^2 + (y準則)$^2$
\]
\[
D^2 = (x_2 - x_1)^2 + (y準則)$^2$
\]
\[
D^2 = (x_2 - x_1)^2 + (y準則)$^2$
\]
\[
D^2 = (x_2 - x_1)^2 + (y準則)$^2$
\]
\[
D^2 = (x_2 - x_1)^2 + (y準則)$^2$
\]
\[
D^2 = (x_2 - x_1)^2 + (y準則)$^2$
\]
\[
D^2 = (x_2 - x_1)^2 + (y準則)$^2$
\]
\[
D^2 = (x_2 - x_1)^2 + (y準則)$^2$
\]
\[
D^2 = (x_2 - x_1)^2 + (y準則)$^2$
\]
\[
D^2 = (x_2 - x_1)^2 + (y準則)$^2$
\]
\[
D^2 = (x_2 - x_1)^2 + (y準則)$^2$
\]
\[
D^2 = (x_2 - x_1)^2 + (y準則)$^2$
\]
\[
D^2 = (x_2 - x_1)^2 + (y準則)$^2$
\]
\[
D^2 = (x_2 - x_1)^2 + (y準則)$^2$
\]
\[
D^2 = (x_2 - x_1)^2 + (y準則)$^2$
\]
\[
D^2 = (x_2 - x_1)^2 + (y準則)$^2$
\]
\[
D^2 = (x_2 - x_1)^2 + (y準則)$^2$
\]
\[
D^2 = (x_2 - x_1)^2 + (y準則)$^2$
\]
\[
D^2 = (x_2 - x_1)^2 + (y準則)$^2$
\]
\[
D^2 = (x_2 - x_1)^2 + (y準則)$^2$
\]
\[
D^2 = (x_2 - x_1)^2 + (y準則)$^2$
\]
\[
D^2 = (x_2 - x_1)^2 + (y準則)$^2$
\]
\[
D^2 = (x_2 - x_1)^2 + (y準則)$^2$
\]
\[
D^2 = (x_2 - x_1)^2 + (y準則)$^2$
\]
\[
D^2 = (x_2 - x_1)^2 + (y準則)$^2$
\]
\[
D^2 = (x_2 - x_1)^2 + (y準則)$^2$
\]
\[
D^2 = (x_2 - x_1)^2 + (y準則)$^2$
\]
\[
D^2 = (x_2 - x_1)^2 + (y準則)$^2$
\]
\[
D^2 = (x_2 - x_1)^2 + (y準則)$^2$
\]
\[
D^2 = (x_2 - x_1)^2 + (y準則)$^2$
\]
\[
D^2 = (x_2 - x_1)^2 + (y準則)$^2$
\]
\[
D^2 = (x_2 - x_1)^2 + (y準則)$^2$
\]
\[
D^2 = (x_2 - x_1)^2 + (y準則)$^2$
\]
\[
D^2 = (x_2 - x_1)^2 + (y準則)$^2$
\]
