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笔者看到2014年上海高考(理工农医类)第22题,有眼前一亮的感觉,考题中的定义“点P_1、P_2被直线l分隔”在课本例题的基础上进一步改编拓展,利用方向距离来刻画数与形的内在关系,既考查数学基础知识,又考查学生的阅读理解能力.笔者对此定义饶有兴趣,对其内涵进行了探究.考题呈现在平面直角坐标系xOy中,对于直线l:ax+by+c=0和点P_1(x_1,y_1)、P_2(x_2,y_2),记η=(ax_1+by_1+c)(ax_2+by_2+c).若η<0,则称点P_1、P_2被直线l分隔.若曲线C与直线l没有公共
The author saw the 22nd question of the Shanghai college entrance examination (agricultural medicine) in 2014. There is a bright feeling in the exam. The definition in the exam “P_1 and P_2 are separated by a straight line l” is further adapted and expanded on the basis of the textbook examples. The directional distance is used to describe the internal relationship between numbers and shapes. It not only examines the basic knowledge of mathematics, but also examines students’ reading comprehension ability. The author is interested in this definition and has explored its connotations. The questions are presented in the plane rectangular coordinate system xOy. For lines l:ax+by+c=0 and points P_1(x_1,y_1), P_2(x_2,y_2), note η=(ax_1+by_1+c)(ax_2+by_2+c). If η<0 , the points P_1, P_2 are said to be separated by a straight line l. If curve C and line l are not public