问题 选择题
平面上A(-2,1),B(1,4),D(4,-3),C点满足
AC
=
1
2
CB
,连DC并延长至E,使|
CE
|=
1
4
|
ED
|,则点E坐标为(  )
A.(-8,-
5
3
B.(-
8
3
11
3
C.(0,1)D.(0,1)或(2,
11
3
答案

设C的坐标是(x,y),由

AC
=
1
2
CB
和A(-2,1),B(1,4)得,

(x+2,y-1)=

1
2
(1-x,4-y),即x+2=
1
2
(1-x)且y-1=
1
2
(4-y),

解得C的坐标是(-1,2),

设E的坐标是(x,y),由|

CE
|=
1
4
|
ED
|和连DC并延长至E知,
DC
=3
CE

把D(4,-3)和C(-1,2)代入得,(-5,5)=3(x+1,y-2),

即3x+3=-5且3y-6=2,解x=-

8
3
,y=
11
3
,则E的坐标是(-
8
3
11
3
).

故选B.

判断题
判断题