3.3.1　两条直线的交点坐标

课时过关·能力提升

一、基础巩固

1.直线2x+3y+8=0和直线x-y-1=0的交点坐标是0(　　)

A.(-2,-1) B.(-1,-2)

C.(1,2) D.(2,1)

解析:解方程组{■(2x+3y+8=0"," @x"-" y"-" 1=0"," )┤得{■(x="-" 1"," @y="-" 2"," )┤

即交点坐标是(-1,-2).

答案:B

2.直线√3 x-y=0与x+y=0的位置关系是(　　)

A.相交但不垂直 B.平行

C.重合 D.垂直

解析:易知A1=√3, B1=-1, A2=1, B2=1,则A1B2-A2B1=√3×1-1×(-1)=√3+1≠0.又A1A2+B1B2=√3×1+(-1)×1=√3-1≠0,则这两条直线相交但不垂直.

答案:A

3.如果两条直线2x+3y-k=0和x-ky+12=0的交点在y轴上,那么k的值为(　　)

A.-24 B.6 C.±6 D.24

解析:在2x+3y-k=0中,令x=0,得y=k/3.将(0"," k/3)代入x-ky+12=0,解得k=±6.

答案:C

4.不论a为何实数,直线(a-3)x+2ay+6=0恒过(　　)

A.第一象限 B.第二象限

C.第三象限 D.第四象限

解析:直线(a-3)x+2ay+6=0可变形为a(x+2y)+(6-3x)=0.由{■(x+2y=0"," @6"-" 3x=0"," )┤得{■(x=2"," @y="-" 1"." )┤