关于平面直角坐标系中最小值问题,因学生对这类问题缺少必要的变换和转化思想,从而在做题时感到无从下手。下面,笔者通过几道例题,提供几种应对这类问题的方法,供参考学习。方法1:作关于坐标轴的对称点,利用两点之间线段最短解决问题。例1如图1,在平面直角坐标系中,点A的坐标为(3,2),点B的坐标为(1,-2),试在y轴上找一点P,使PA+PB的长度最小,并求出该最小值。解:作点B关于y轴的对称B′,在y轴上任意取一点P′,联结 With regard to the minimum value in the rectangular Cartesian coordinate system, students lack the necessary transformation and transformational thinking on such issues and thus find themselves unable to start their task. Below, I through several examples, provide several ways to deal with such issues for reference. Method 1: Make a point about the axis of symmetry, using the shortest line between the two points to solve the problem. Example 1 As shown in Figure 1, in Cartesian coordinate system, the coordinate of point A is (3,2) and the coordinate of point B is (1, -2). Try to find a point P on the y-axis to make PA + PB The minimum length, and find the minimum value. Solution: for point B on the y-axis symmetry B ’, on the y-axis take a point P’, the connection