c4568735453:高中数学(人教A版)必修2随堂优化训练:3.2.1 直线的点斜式方程(含答案)

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3.2 直线的方程 3.2.1 直线的点斜式方程

1.已知直线 l 的方程为 y=-x+1,则该直线 l 的倾斜角为( ) A.30° B.45° C.60° D.135° 2.过点(4,-2),倾斜角为 120° 的直线方程是( ) A. 3x+y+2-4 3=0 B. 3x+3y+6+4 3=0 C.x+ 3y-2 3-4=0 D.x+ 3y+2 3-4=0 3.已知直线的方程是 y+2=-x-1,则( ). A.直线经过点(2,-1),斜率为-1 B.直线经过点(-2,-1),斜率为 1 C.直线经过点(-1,-2),斜率为-1 D.直线经过点(1,-2),斜率为-1 4.直线 l 过点(1,-2)且与直线 2x-3y-1=0 垂直,则 l 的方程是( ) A.3x+2y+1=0 B.3x+2y+7=0 C.2x-3y+5=0 D.2x-3y+8=0 5.直线 kx-y+1-3k=0,当 k 变化时,所有直线恒过定点( ). A.(0,0) B.(3,1) C.(1,3) D.(-1,-3) 6.如果直线 l 沿 x 轴负方向平移 3 个单位长度,再沿 y 轴正方向平移 1 个单位长度后, 又回到原来的位置,则直线 l 的斜率是________. 4 7.已知直线经过点 A(3,-2),斜率为- ,求该直线方程. 3

1 8.已知直线 l:mx+ny+1=0 平行于直线 m:4x+3y+5=0,且 l 在 y 轴上的截距为 , 3 则 m,n 的值分别为( ) A.4,3 B.-4,3 C.-4,-3 D.4,-3 9.已知△ABC 的顶点坐标分别为 A(1,3),B(5,7),C(10,12),求 BC 边上的高所在的直 线的方程.

10.已知直线 l 在 y 轴上的截距为-3 且它与两坐标轴围成的三角形的面积为 6,求直 线 l 的方程.

3.2.1 直线的点斜式方程 1.D 2.A 解析:k=tan120° ,故直线的点斜式方程为 y+2=- 3(x-4),化简得 3x+y +2-4 3=0. 3.C 4.A 5.B 1 6.- 解析:设直线 l 的方程为 y=kx+b,由题意,得 y=k(x+3)+b+1 与 y=kx+b 3 1 相同,∴3k+1=0,k=- . 3 4 4 7.解:经过点 A(3,-2),并且斜率为- 的直线方程的点斜式是 y+2=- (x-3),即 3 3 4x+3y-6=0. m 1 4 8.C 解析:直线 mx+ny+1=0 可化为 y=- x- ,4x+3y+5=0 可化为 y=- x n n 3 m 4 - =- , ? n 3 ?m=-4, 5 1 - ,由于 l∥m,l 在 y 轴上的截距为 ,所以 即? 3 3 1 1 ?n=-3. ? - = , n 3

? ? ?

12-7 9.解:kBC= =1,因此 BC 边上的高所在的直线的斜率为-1,直线方程为 y-3 10-5 =-(x-1),即 x+y-4=0. 10.解:由已知得直线 l 的斜率存在,且不等于零. 设直线 l 的方程:y=kx-3. 3 当 y=0 时,x= . k 1 ?3? 3 所以 · · 3=6,解得 k=± . 2 ? k? 4 3 故所求直线方程为 y=± x-3. 4


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