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数学
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向量数量积..
已知正方形ABCD,点A(-2,3),C(1,1),求顶点D的坐标.
人气:174 ℃ 时间:2020-03-19 01:33:17
解答
设D(x,y)
则AD=(x+2,y-3),CD=(x-1,y-1)
∵ 是正方形ABCD
∴ AD•CD=0且|AD|=|CD|
∴ (x+2)(x-1)+(y-3)*(y-1)=0且 (x+2)²+(y-3)²=(x-1)²+(y-1)²
∴ (x+2)(x-1)+(y-3)*(y-1)=0且 6x-4y+11=0
解方程,得到 x=1/2,y=7/2或x=-3/2.y=1/2
即 D(1/2,7/2)或D(-3/2,1/2)
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