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现行六年制重点中学数学课本《解析几何》中,关于点P(x_0,y_0)到直线l:Ax+By+C=0的距离公式的推导,改变了原试用本教材中根据点线距离的定义,思路自然,比旧教材中由直线的法线式推导点线距离公式更为优越。但是,教材对点线距离公式d=±(Ax_0+By_0+C)/(A~2+B~2)~(1/2)中“±”号的确定没给出一定的法则,因而使公式的应用受到一定的限制,使得在解决有关证明或轨迹问题时发生困难,大大削弱了公式的使用价值。例如,用解析法证明“等边三角形内任意一点到三边距离之和等于三角形的高”这一命题时,若不确定公式中的正负号而使用书上所给出的距离公式,就会遇到较大的困难。我们认为,在讲授这一公式时应补充符号法则,以
In the current six-year key middle school mathematics textbook “Analytic Geometry,” the derivation of the distance formula from the point P(x_0,y_0) to the straight line l:Ax+By+C=0 changes the distance according to the dotted line in the original trial textbook. The definition of the idea, the natural way of thinking, is superior to the formula derived from the normal line of the straight line in the old textbook. However, the textbook does not give a certain rule for the determination of the “±” in the dot-line distance formula d=±(Ax_0+By_0+C)/(A~2+B~2)~(1/2). The application of the formula is subject to certain restrictions, which make it difficult to solve problems related to certification or trajectory, which greatly weakens the use value of the formula. For example, using analytical methods to prove that the sum of distances from any point to three sides in an equilateral triangle is equal to the height of the triangle, if you use the distance formula given in the book if you do not determine the sign in the formula, Will encounter greater difficulties. We believe that when we teach this formula, we should add the rule of thumb to