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[img]ct_gre5image020[/img]AB=BC,AC=BD; What are the coordinates of point B in t
[img]ct_gre5image020[/img]AB=BC,AC=BD; What are the coordinates of point B in t
游客
2025-02-24
6
管理
问题
AB=BC,AC=BD; What are the coordinates of point B in the xy-plane above?
选项
A、(6,12)
B、(6,28)
C、(8,20)
D、(12,20)
E、(14,28)
答案
B
解析
在上面的xy平面中,B点的坐标是多少?
解:本题的正确答案为(B)。由AB=BC,可推知△ABC为一等腰三角形,BD垂直AC且平AC,则D点坐标为x=(-8+20)/2=6,D点在x轴上,所以其纵坐标等于0。B点与D点在同一条与y轴平行的直线上,所以B点的横坐标也为6;A和C两点都在x轴上,所以它们之间的距离等于两点的横坐标的差的绝对值,即AC=|-8-20|=28;又由BD=AC可知,B点纵坐标为28。综上所述B点的坐标(6,28)
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