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近几年来,全国各省市中考数学试卷经常有的一个考点是:已知平行四边形三个顶点的坐标,求第四个顶点的坐标。给出的参考答案往往是从几何的角度考虑问题,先尝试画出符合要求的所有点,然后通过几何推理,推导出第四个顶点的坐标。这样做的难点是学生画不出符合要求的所有点,经常会有漏掉的情况,或者由于推理能力差,不能求出点的坐标。那么,能不能建立解决这类问题的数学模型,不用画图,直接套用公式计算,就能使难题获解呢?下面笔者将整理的公式提供给大家,以供参考。
In recent years, one of the most frequently used test points for mathematics examinations in various provinces and cities across the country is: Know the coordinates of the three vertices of a parallelogram and find the coordinates of the fourth vertex. The reference answer given is often considered from a geometric point of view. The first attempt is to draw all the points that meet the requirements, and then through geometric reasoning, the coordinates of the fourth vertex are derived. The difficulty in doing this is that students cannot draw all the points that meet the requirements, and often there are missed cases, or because the reasoning ability is poor, the coordinates of the points cannot be found. Then, can we establish a mathematical model to solve this kind of problem, without drawing, directly applying formula calculations, we can solve the problem? The following author will provide you with formulas for reference.