《数理天地》曾刊登文章《一例说明坐标系中三角形面积的求法》,读罢受益匪浅.作者给出了四种方法,均为通过求三角形的面积,最终求出点M的坐标.笔者通过研究发现,问题也可以不求面积而求出点M的坐标,而且这种方法具有一定的代表性.下面给出具体过程,以供参考.问题如图1,在平面直角坐标系xOy中,已知点A(-1,0)、B(0,2)、C(3,0),直线a “Mathematical World” has published an article, “An Example of the triangle area in the coordinate system of seeking,” read a lot of benefits.The author gives four methods, are obtained by finding the area of ​​the triangle, and finally find the coordinates of the point M. Author Through the study found that the problem can not seek the coordinates of the point M, and this method has a certain representation. The following is a specific process for reference. The problem shown in Figure 1, Cartesian coordinates in the plane xOy , Known points A (-1,0), B (0,2), C (3,0), line a