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在学习函数及其图像时,图像上的点和平面直角坐标系中其它的一些点可构成一些三角形,而求这些三角形的面积是中考中常出现的题型.现在就举例剖析一下这些三角形面积的求法.大背景:已知二次函数y=x2-2x-3的图像(如图1),求(1)对称轴,(2)顶点D的坐标,(3)与y轴交点C的坐标,(4)与x轴的交点A、B的坐标.这是二次函数的基础知识,很容易求得:(1)对称轴x=1,(2)顶点坐标D(1,-4),(3)与y轴交点的坐标C(0,-3),(4)与x轴的交点的坐标A(-1,0)、B(3,0).一、巧用坐标轴解决面积问题1.以x轴上的线段为底图1问题1如图1,在背景问题的基础上求△ABC的面积.解∵点A、B都在x轴上,∴求△ABC的面积要以AB为底,S△ABC=12|AB|·|CO|=12×4×3=6.
In studying the function and its image, some points in the image and other points in the Cartesian coordinate system can form some triangles, and finding the area of these triangles is a common problem in the middle school entrance examinations. Now analyze the area of these triangles (1) axis of symmetry, (2) the coordinates of the vertex D, (3) the coordinates of the point of intersection C with the y-axis , (4) the coordinates of the intersection points A and B with the x axis, which is the basic knowledge of the quadratic function and is easy to find: (1) Axis of symmetry x = 1, (2) , (3) the coordinates of the intersection of the y-axis C (0, -3), (4) and the x-axis coordinates A (-1,0), B (3,0) Area problem 1. Take the line segment on the x-axis as the base Figure 1 Question 1 As shown in Figure 1, on the basis of the background problem, find the area of ABC. Solution points A, B are on the x-axis, AB to be the end, S △ ABC = 12 | AB | · | CO | = 12 × 4 × 3 = 6.