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高中代数教材甲种本二册习题六有这样一道题:如果a、b为不全为0的实数,则有x~2+y~2≥(ax+by)~2/a~2+b~2 (这是柯西—施瓦尔兹不等式的特例) 证明从略.我们用它来推导点到直线之距离公式。
High School Algebra Textbook A type of this two-volume exercise 6 There is such a question: If a, b are real numbers not all 0, then there are x~2+y~2≥(ax+by)~2/a~2+b~ 2 (This is a special case of the Cauchy-Schwarzian inequality) Proof. We use it to derive the formula for distance from point to line.