问题 填空题
已知两点A(-1,0),B(2,3),点C满足2
AC
=
CB
,则点C的坐标是______,
AB
AC
=______.
答案

∵点C满足2

AC
=
CB
,∴2(
OC
-
OA
)=
OB
-
OC
,得到
OC
=
1
3
(2
OA
+
OB
)
=
1
3
[2(-1,0)+(2,3)]
=(0,1)

AB
=(2,3)-(-1,0)=(3,3),
AC
=(0,1)-(-1,0)=(1,1),

AB
AC
=3×1+3×1=6.

故答案分别为(0,1),6.

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