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在解析几何求轨迹的问题中,有些题目适合利用复数来求解,从而避免了繁冗的过程,使之简化. 我就遇到过以下两道题,可借助复数来解. 例1 在平面直角坐标系中,有折线y=|x|,三角形ABC中,∠ACB=90°.CA=CB=2~(1/2),顶点A、B分别在射线y=-x(x<0)与y=x(x>0)上运动,点C位于y>|x|的区域中,求三角形ABC重心G的轨迹方程. 解设C(xc,yc),A(xa,-xA),B(xB,xB)、如图
In the problem of solving geometry for trajectory, some topics are suitable for solving using complex numbers, thereby avoiding the tedious process and simplifying it. I have encountered the following two problems, which can be solved by means of complex numbers. Example 1 In the Cartesian coordinates In the system, there is a polyline y=|x|, in the triangle ABC, ∠ACB=90°.CA=CB=2~(1/2), the vertices A and B are respectively in the ray y=-x(x<0) and y=x(x>0) moves, point C lies in the area of y>|x|, finds the trajectory equation of triangle ABC center of gravity G. Solution C(xc,yc),A(xa,-xA),B (xB,xB), figure