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33325kkcom:高一数学直线与方程试卷

高二数学《直线与方程》测试卷
班级: 一、选择题 1.下列直线中与直线 x-2y+1=0 平行的一条是 A.2x-y+1=0 B.2x-4y+2=0 C.2x+4y+1=0 D.2x-4y+1=0 2.已知两点 A(2,m)与点 B(m,1)之间的距离等于 13 ,则实数 m= A.-1 B .4 C.-1 或 4 D.-4 或 1 姓名: 学号: 总分:

3.过点 M(-2,a)和 N(a,4)的直线的斜率为 1,则实数 a 的值为 A.1 B .2 C .1 或 4 D.1 或 2

4.如果 AB>0,BC>0,那么直线 Ax―By―C=0 不经过的象限是 A.第一象限 B.第二象限 C.第三象限 D.第四象限

5.直线 l:mx-m2y-1=0 经过点 P(2,1),则倾斜角与直线 l 的倾斜角互为补角的一条直 线方程是 A.x―y―1=0 B.2x―y―3=0 C.x+y-3=0 D.x+2y-4=0 6.已知两条平行直线 l1 : 3x+4y+5=0,l2 : 6x+by+c=0 间的距离为 3,则 b+c= A.-12 B.48 C.36 D.-12 或 48

7.过点 P(1,2),且与原点距离最大的直线方程是 A.x+2y-5=0 C.x+3y-7=0 B.2x+y-4=0 D.3x+y-5=0
1? ?1 D. ? ,- ? 2? ?6

8.a,b 满足 a+2b=1,则直线 ax+3y+b=0 必过定点 1? ? 1 1? ?1 ?1 1? A . ?- , ? B. ? ,- ? C. ? , ? 6? ? 6 2? ?2 ?2 6? 题号 答案 二、填空题 1 2 3 4 5 6 7

8

得分

9.已知直线 AB 与直线 AC 有相同的斜率,且 A(1,0),B(2,a),C(a,1),则实数 a 的 值是____________. 10.已知点(a,2)(a>0)到直线 x-y+3=0 的距离为 1,则 a 的值为________. 11.已知直线 ax+y+a+2=0 恒经过一个定点,则过这一定点和原点的直线方程是 ____________________. 12.已知实数 x,y 满足 5x+12y=60,则 x 2 + y 2 的最小值等于____________.

三、解答题 13.求斜率为

3 ,且与坐标轴所围成的三角形的周长是 12 的直线方程. 4

14. 过点 P(1, 2)的直线 l 被两平行线 l1 : 4x+3y+1=0 与 l2 : 4x+3y+6=0 截得的线段长|AB| = 2 ,求直线 l 的方程.

15.已知方程(m2―2m―3)x+(2m2+m-1)y+6-2m=0(m∈R). (1)求该方程表示一条直线的条件; (2)当 m 为何实数时,方程表示的直线斜率不存在?求出这时的直线方程; (3)已知方程表示的直线 l 在 x 轴上的截距为-3,求实数 m 的值; (4)若方程表示的直线 l 的倾斜角是 45° ,求实数 m 的值.

16.△ABC 中,已知 C(2,5),角 A 的平分线所在的直线方程是 y=x,BC 边上高线所在的 直线方程是 y=2x-1,试求顶点 B 的坐标.


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