题目内容
设P1(4,-3),P2(-2,6),且P在P1P2的延长线上,使
A.(-8,15)
B.(0,3)
C.(-
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
D.(1,

【答案】分析:解法一:设分点P(x,y),由题意知
=-2
,利用向量相等的条件得 (x-4,y+3)=-2(-2-x,6-y),解出点P坐标.
解法二:设分点P(x,y),由
=-2
,P分有向线段P1P2成的 比 λ=-2,代入定比分点坐标公式解点P坐标.
解答:解:解法一:设分点P(x,y),由题意知
=-2
,P分有向线段P1P2成的 比 λ=-2,
根据向量相等的条件得:(x-4,y+3)=-2(-2-x,6-y),
x-4=2x+4,y+3=2y-12,∴x=-8,y=15,
∴P(-8,15).
解法二:设分点P(x,y),∵
=-2
,P分有向线段P1P2成的 比 λ=-2,
代入定比分点坐标公式得:
∴x=
=-8,
y=
=15,
∴P(-8,15)
故选A.
点评:本题考查利用向量相等求点P的坐标,或利用定必分点坐标公式求点P的坐标的方法.


解法二:设分点P(x,y),由


解答:解:解法一:设分点P(x,y),由题意知


根据向量相等的条件得:(x-4,y+3)=-2(-2-x,6-y),
x-4=2x+4,y+3=2y-12,∴x=-8,y=15,
∴P(-8,15).
解法二:设分点P(x,y),∵


代入定比分点坐标公式得:
∴x=

y=

∴P(-8,15)
故选A.
点评:本题考查利用向量相等求点P的坐标,或利用定必分点坐标公式求点P的坐标的方法.

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