问题 选择题
在梯形ABCD中,ABCD,AB=2CD,M,N分别是CD,AB的中点,设
AB
=
a
AD
=
b
.若
MN
=m
a
+n
b
,则
n
m
=(  )
A.-
1
4
B.-4C.
1
4
D.4
答案

∵梯形ABCD中,ABCD,AB=2CD,M,N分别是CD,AB的中点,

AN
=
1
2
AB
DM
=
1
2
DC
=
1
4
AB

AM
=
AD
+
DM
=
AD
+
1
4
AB

可得

MN
=
AN
-
AM
=
1
2
AB
-(
AD
+
1
4
AB
)=
1
4
AB
-
AD

AB
=
a
AD
=
b
.∴
MN
=
1
4
a
-
b
=m
a
+n
b

可得m=

1
4
,n=-1,
n
m
=
-1
1
4
=-4

故选:B

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