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In the coordinate plane, points A and B are endpoints of a diameter of a circle
In the coordinate plane, points A and B are endpoints of a diameter of a circle
游客
2025-02-24
31
管理
问题
In the coordinate plane, points A and B are endpoints of a diameter of a circle with center ( -2,1). If the coordinates of A are ( -5,5) , what are the coordinates of B?
选项
A、(0,0)
B、(3,-2)
C、(3,-1)
D、(2,-2)
E、(1,-3)
答案
E
解析
在坐标平面上,A和B两点是以(-2,1)为圆心的直径的端点(endpoint)。若A点坐标为(-5,5),那么B点的坐标是多少?
解:本题的正确答案为(E)。设圆心坐标(X0,Y0),因为圆心是A和B中点,所以由平面内任两点中点的坐标公式可得:XA+XB=2 X0,YA+YB=2 Y0。代入圆心与B点坐标,可求得B点坐标为(1,-3)。
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