In the coordinate plane, points A and B are endpoints of a diameter of a circle

游客2025-02-24 29

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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