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2002年浙江省绍兴市中考数学试卷第26题: 如图,巳知平面直角坐标系中三点A(4,0),B(0,4),P(x,0)(x<0),作PC⊥PB交过点A的直线l于点C(4,y)。(1)求y关于x的函数解析式; (2)当x取最大整数时,求BC与PA的交点Q的坐标。 这是一道数形结合的典型试题,其设计精巧,解法丰富多彩,既可利用相似三角形知识求解,也可利用勾股定理、三角函数、射影定理、全等三角形,直线方程等知识求解。
2002 Zhejiang Province Shaoxing City Entrance Examination Math Question 26: As shown in the figure, we know three points A(4,0), B(0,4), P(x,0) (x<0) in the plane rectangular coordinate system. , for PC ⊥ PB cross point A line l at point C (4, y). (1) Find the function analytical formula of y with respect to x; (2) When x takes the largest integer, find the coordinates of the intersection Q of BC and PA. This is a typical test with a combination of numbers and shapes. Its design is sophisticated and the solution is rich and varied. It can be solved by using knowledge of similar triangles, or by using Pythagorean theorem, trigonometric function, projective theorem, congruent triangles, and linear equations.