问题 选择题
已知直线:A1x+B1y+C1=0(C1≠0)与直线l2:A2x+B2y+C2=0(C2≠0)交于点M,O为坐标原点,则直线OM的方程为(  )
A.(
A1
C1
-
A2
C2
)x+(
B1
C1
-
B2
C2
)y=0
B.(
A1
C1
-
A2
C2
)x-(
B1
C1
-
B2
C2
)y=0
C.(
C1
A1
-
C2
A2
)x+(
C1
B1
-
C2
B2
)y=0
D.(
C1
A1
-
C2
A2
)x-(
C1
B1
-
C2
B2
)y=0
答案

A1
C1
x+
B1
C1
y+1=0,

l2

A2
C2
x+
B2
C2
y+1=0,

两式相减得(

A1
C1
-
A2
C2
)x+(
B1
C1
-
B2
C2
)y=0.

∵点O、M的坐标都满足该直线的方程,

∴点O、M都在该直线上,

∴直线OM的方程为(

A1
C1
-
A2
C2
)x+(
B1
C1
-
B2
C2
)y=0.

故选A.

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