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在平面直角坐标系中,处在不同位置的点具有不同的坐标特征,利用这些点的坐标特征可以准确快速地解决问题,现举例说明.一、各界限内的点的坐标特征若点Px(x,y)在第一象限,则x>0,y>0;若点P(x,y)在第二象限,则x<0,y>0;若点P(x,y)在第三象限,则x<0,y<0;若点P(x,y)在第四象限,则x>0,y<0.例1若点P(a,b)在第四象限,则点Q(-a,b-1)在().A.第一象限B.第二象限C.第三象限D.第四象限解析:因为点P(a,b)在第四象限,根据第四象限内点的坐标特征,可知a>0,b<0,所以-a<0,b-1<0,所以点Q(-a,b-1)在第三象限.
In plane Cartesian coordinate system, the points at different positions have different coordinate features, the coordinate features of these points can be used to solve the problem accurately and quickly, and the examples are given as follows: 1. Coordinate Characteristics of Points within Each Boundary If Px ( x> 0, y> 0; if the point P (x, y) is in the second quadrant, then x <0, y> 0; If the point P (x, y) is in the fourth quadrant, then x> 0, y <0. Example 1 If point P (a, b) is in the fourth quadrant, Point A. The first quadrant B. The second quadrant C. The third quadrant D. The fourth quadrant Analysis: Since the point P (a, b) is in the fourth quadrant, the point Q (-a, b- Therefore, the point Q (-a, b-1) is in the third quadrant when -a <0 and b-1 <0.