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在人民教育出版社出版的普通高中课程标准实验教科书《数学4(必修)》第99页,有一个例8:设点P是线段P_1P_2上的一点,P_1P_2的坐标分别是(x_1,y_1),(x_2,y_2).(1)当点P是线段P_1P_2的中点时,求点P的坐标;(2)当点P是线段P_1P_2的一个三等分点时,求点P的坐标.在教学中,两个问题我们分别由OP=1/2(OP_1+OP_2)、OP=2/3OP_1+OP_2或OP=1/3OP_1+2/3OP_2得到点P的坐标,在让学生观察上述式子时,学生得到一个关于平面向量的结论:结论1.已知O,A,B三点不共线,点P满足:OP=
In People’s Education Publishing House published ordinary high school curriculum standard experimental textbook “mathematics 4 (compulsory)” on page 99, there is an example 8: set point P is a point on the line P_1P_2, P_1P_2 coordinates (x_1, y_1) (x_2, y_2). (1) Find the coordinates of point P when point P is the midpoint of line segment P_1P_2; (2) Find the coordinates of point P when point P is a third-degree point of line segment P_1P_2. Teaching, the two problems we get the coordinates of point P by OP = 1/2 (OP_1 + OP_2), OP = 2 / 3OP_1 + OP_2 or OP = 1 / 3OP_1 + 2 / 3OP_2, let the students observe the above formula , The student gets a conclusion about plane vector: Conclusion 1. Known O, A, B three points are not collinear, the point P satisfies: OP =