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反比例函数y=k/x的本质特征是:两个变量y与x的乘积是一个常数k.由此不难得出反比例函数的一个重要性质:性质如图1,点P(x,y)是反比例函数y=-k/x上任意一点,过点P作PA⊥x轴于点A,作PB⊥y轴于点B,则S_(长方形AOBP)=|k|,S_(△PAO)=1/2|k|.下面举例说明上述结论的应用.一、正向应用例1如图2,点A在双曲线y=1/x上,点B在双曲线y=3/x上,且AB∥x轴,C、D在x轴上,若四边形ABCD的形状为矩形,则它的面积为____.
The essential feature of the inverse function y = k / x is that the product of the two variables y and x is a constant k. It is therefore not hard to come to an important property of the inverse function: the properties are shown in Figure 1, where point P (x, y) is The inverse proportion function y = -k / x at any point, over the point P for the PA ⊥ x axis at point A, for PB ⊥ y axis at point B, S_ (rectangular AOBP) = | k |, S_ (PAO) = 1/2 | k | The following is an example of the application of the above conclusion: 1. Forward Application Example 1 As shown in Figure 2, point A is on a hyperbola y = 1 / x, point B is on a hyperbola y = 3 / x, And AB∥x axis, C, D on the x-axis, if the quadrilateral ABCD shape is rectangular, then its area is ____.