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在平面几何题中,适当的建立直角坐标系,利用代数的方法解决几何问题,即解析法,有时会显得更简洁高效.现以近年中考压轴题为例,分析说明解析法之妙.例1(2013泰州)如图1,在矩形ABCD中,点P在边CD上,且与C、D不重合,过点A作AP的垂线与CB的延长线相交于点Q,连结PQ,M为PQ中点.若AD=10,AB=a,DP=8,随着a的大小的变化,点M的位置也在变化.当点M落在矩形ABCD外部时,求a的取值范围.分析本题将矩形、三角形、动点、参数相结合,考察学生利用相似解决问题的综合
In the plane geometry, the right to establish rectangular coordinate system, the use of algebraic methods to solve the geometric problems, that is, analytic methods, and sometimes will appear more concise and efficient. Now in recent years, the test pressure axis as an example, analysis and analysis of the wonderful method. (2013 Taizhou) As shown in Figure 1, in the rectangular ABCD, the point P is on the side CD and does not overlap with C and D. The vertical line passing through point A and the extended line of CB intersect at the point Q, connecting PQ and M PQ midpoint. If AD = 10, AB = a, DP = 8, with the size of a change, the location of the point M is also changing when the point M falls outside the rectangle ABCD, find the value of a range Analysis of the problem will be a rectangle, triangle, moving point, a combination of parameters, examine the students to use a similar solution to the problem