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学了平面直角坐标系后,我发现,平面直角坐标系中那些让人“糊涂”的点也很奇特,下面,就让我来说一说坐标系里这些令人眼花缭乱的点吧.一、平面直角坐标系中的点关于坐标系的四条对称轴对称设点A(a,b)在第一象限,则a>0,b>0.如图1,我们可直接看出A关于x轴对称的点的坐标是(a,-b),关于y轴对称的点的坐标是(-a,b).如图2,可论证A关于一、三象限角平分线对称的点的坐标是(b,a),A关于二、四象限角平分线对称的点的坐标是(-b,-a).
After learning the plane rectangular coordinate system, I found that the “confused” points in the plane rectangular coordinate system are also very strange. Now, let me talk about these dazzling points in the coordinate system. 1. Points in the plane rectangular coordinate system Symmetrically set the four symmetry axes of the coordinate system A (a, b) in the first quadrant, then a> 0, b> 0. As shown in Figure 1, we can directly see A The coordinate of the x-axis symmetry point is (a,-b), and the coordinate of the symmetry point about the y-axis is (-a,b). As shown in Figure 2, it can be demonstrated that A is symmetrical about the bisector of the one and three quadrant angles. The coordinates are (b, a), and the coordinates of point A that is symmetric about the bisector and quadrant bisector are (-b,-a).