点到直线的距离公式是高中解析几何课本中最重要的也是最精彩的公式之一 ,它的推导思路多样 ,方法灵活 .据笔者不完全的资料收集已有十余种以上 ,有几何方法 ,也有代数方法 ,但不是任何一种数学推导方法都能做为教学设计的推导方法 .如代数方法中的用拉格朗日恒等式、柯西不等? The point-to-line distance formula is one of the most important and exciting formulas in high school analytic geometry textbooks. It has a variety of derivation ideas and methods. According to the author’s incomplete data collection, there are more than ten kinds of geometrical methods. There are also algebraic methods, but not any mathematical derivation method can be used as a derivation method for instructional design. For example, using Lagrange’s identity and Cauchy’s in algebraic methods?