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题目如图1所示,一次函数y=kx-2(k>0)与双曲线y=k/x在第一象限内的交点为R,与x轴、y轴的交点分别为P、Q,过点R作RM⊥x轴于肘点,若△OPQ与△MPR的面积相等,则K的值等于多少?这道试题是《中小学数学》(初中版)2012年第5期毛立武《给三角形全等补充一个判定定理》(简称“毛文①”)一文中的一个例题,毛文①中指出:从这道题的解答来看,必须证明△OPQ≌△MPR,这是题中的隐含条件,假如不证明或不利用△OPQ≌△MPR,借助其它条件,是绝对求不出k的值.
The subject is shown in Figure 1. The intersection point of the linear function y = kx-2 (k> 0) and the hyperbolic y = k / x in the first quadrant is R, and the intersection with the x axis and the y axis is P, Q , The point R for RM ⊥ axis at the elbow point, if △ OPQ and △ MPR area equal, the value of K is equal to how much? This question is “elementary and secondary mathematics” (junior high school edition) 2012 fifth period Mao Liwu “ An example of a sentence in the article ”Supplementing a Judgment Theorem for Triangle Equality“ (referred to as ”Mao Wen ①") pointed out in Mao Wen’s paper that from the solution to this question, it must be proved that △ OPQ≌ △ MPR, which is The implied conditions of the problem, if you do not prove or do not use △ OPQ≌ △ MPR, with other conditions, is absolutely not k value.