论文部分内容阅读
众所周知,曲线f(x,y)=0关于x轴对称的曲线方程是f(x,-y)=0,关于y轴对称的曲线方程是f(-x,y)=0,关于原点成中心对称的曲线方程是f(-x,-y)=0由此想到曲线f(x,y)=0关于任何已知直线ax+by+c=0成轴对称的曲线方程是什么形式?关于任何已知点M(a,b)成中心对称的曲线方程又是什么形式?这就是本文要探讨的问题。 先看一名中学生对下面一道习题的奇妙解法。题目是:“求直线3x-4y+2=0关于直线x-y+3=0成轴对称的直线方程。” 解 由x-y+3=0,得x=y-3,y=x+3,同时代入3x-4y+2=0中,得3(y-3)-4(x+3)+2=0,即4x-3y+19=0。此即为所求的对称直线方程。
It is well known that the curve f (x, y) = 0 is symmetric with respect to the x-axis and f (x, -y) = 0 with the symmetry curve f The centrosymmetric curve equation is f (-x, -y) = 0 It follows that the curve f (x, y) = 0 What is the form of an axisymmetric curve equation for any given straight line ax + by + c = 0? What is the form of a curvilinear equation that is centrosymmetric about any known point M (a, b)? This is the problem to be explored in this article. Look at a middle school students a wonderful solution to the following problem. The topic is: “Find a straight line equation with straight line 3x-4y + 2 = 0 on axis x-y + 3 = 0 axisymmetric.” Solution by x-y + 3 = 0, we get x = y-3, y = x +3 and 3x-4y + 2 = 0, 3 (y-3) -4 (x + 3) + 2 = 0, that is, 4x-3y + 19 = 0. This is the result of the symmetrical linear equation.