(完整word版)高中数学直线方程(word文档良心出品).pdf

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1、1 一、直线的倾斜角和斜率A如何求直线的倾斜角和斜率1.设直线l过坐标原点O，它的倾斜角为，如将l绕坐标原点按逆时针方向旋转4，得到直线1l，那么直线1l的倾斜角为。2.将直线:22lyx向右平移3 个单位，向上平移2 个单位得到直线1l，则1l的方程为。B三点共线问题3.已知0a，若平面内三点23(1,),(2,),(3,)AaBaCa共线，则a。4.若三点(2,2),(,0),(0,)(0)AB aCbab共线，则11ab。5.已知三点(1,1),(3,3),(4,5)ABC，求证：三点在同一直线上。（分别用：距离公式法、斜率公式法、直线方程证明）C直线斜率的取值范围6.已知两点(3,4)

2、,(3,2)AB，过点(2,1)P的直线l与线段 AB 有公共点，求直线l的斜率k的取值范围。7.直线20axy与连接(3,1),(1,4)AB的线段相交，则a的取值范围是。8.已知矩形ABCD 中，(4,4),(5,7)AD，中心E 在第一象限内且与y轴的距离为1 个单位。动点(,)P x y沿矩形一边BC 运动，求yx的取值范围。二、直线的方程A各种形式的直线方程点斜式11()yyk xx斜截式ykxb两点式112121yyxxyyxx截距式1xyab一般式0A xB yC（220AB）（讨论：能否适用于垂直x轴或y轴及过原点的直线）1.直线l过点(2,1)M，且分别与,x y轴的正半轴交

3、于,A B两点，O 为坐标原点，当AOB的面积最小时，求直线l的方程。2.已 知 两 直 线111:10la xb y和222:10la xb y的 交 点 为(2,3)P，则 过 两 点111222(,),(,)QabQab的直线方程是。3.对于直线l上任意一点(,)x y，点(42,3)xy xy仍在直线l上，求直线l的方程。4.直线220 xy绕它与y轴的交点逆时针旋转2，所得的直线方程是。5.经过点(1,2)A，并且在两坐标轴上的截距的绝对值相等的直线有多少条？2 B三角形面积问题6.经过点(3,4)P作直线l，l与两坐标轴围成的三角形的面积为3，求直线l的方程。7.直线l过点(6,4

4、)P，与x轴正半轴交于A 点，与y轴正半轴交于B 点，O 为坐标原点。若M 为 AB 上一点，且直线OM 的斜率为4，当OAM的面积 S 最小时，求点M 的坐标。C恒过定点问题8.已知直线:120lkxyk。证明：直线l过定点。（方法 1：方程法方法 2：特例法）9.已知直线:()()20lab xab y，其中,a b满足320ab。求证：直线l恒过一定点。D最值问题10.已知(1,0),(1,0)MN，点 P为直线210 xy上动点，求22PMPN的最小值。11.求2222413yxxxx的最小值及相应的x值。12.已知定直线:4lyx和定点(6,4)P，点 Q 为第一象限内的点，且在直线

5、l上，直线 PQ 交x轴正半轴于点 M，求当OMQ的面积最小时Q 点的坐标。E确定直线过象限问题12.若0,0ACBC，则直线0AxByC不通过第象限。13.若直线(32)80axy不过第二象限，则实数a的取值范围是。F线段内分点14.已知ABC，(2,1),(2,3),(6,7)ABC，求 AC 边上中线所在直线的方程。15.过点(1,2)P引一条直线l，使它到两点(2,3),(4,5)AB的距离相等，求直线l的方程。16.ABC的顶点坐标为(3,4),(6,0),(5,2)ABC，求A的平分线AT 所在直线方程。三、两条直线的位置关系A两条直线的各种关系设两直线为：1111:0lA xB

6、yC11()yk xb2222:0lA xB yC22()yk xb两直线平行：1221A BA B且1221A CAC两直线垂直：121k k或12120A AB B对称问题：（1）求点关于点的对称点（2）求直线关于点的对称直线（3）求点关于直线的对称点（4）求直线关于直线的对称直线文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z

7、7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3

8、HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z

9、7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3

10、HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z

11、7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3

12、HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G13 BAl2l1COBAyPx两直线夹角：2112tan1kkk k点到直

13、线的距离：点00(,)P xy到直线:0lAxByC的距离为0022AxByCdAB平行直线间距离：两平行直线为：11:0lAxByC22:0lAxByC两直线间距离为：2122CCdABB两直线平行问题1.过点(1,4)A，且与直线2350 xy平行的直线的方程。2.111(,)Pxy是 直 线:(,)0lfxy上 的 一 点，222(,)Pxy是 直 线l外 一 点，则 方 程1122(,)(,)(,)0f x yf xyf xy所表示的直线 l与直线l的位置关系为。C两直线垂直问题3.已知直线1:42laxy与直线2:250lxyb垂直，点(1,)c为垂足，则abc。4.原点 O 在直线

14、l上的射影为(1,2)A，则直线l的方程为。D有关对称问题主要步骤：1.在所求曲线上任选一点(,)M x y；2.求出这点关于中心或轴的对称点00(,)Mxy与(,)M x y之间的关系；3.将00(,)xy代入已知曲线方程，求出曲线(,)0g x y5.已知两点11(,)Pxy和11(1,1)Qyx关于直线l对称，求直线l的方程。6.如图，已知ABC的一个顶点(4,1)A，它的两条角平分线所在直线的方程分别为1:10lxy和2:10lx，求 BC 边所在直线的方程。7.过点(2,3)，斜率12k射出的光线射到y轴上，则反射光线所在的直线方程为。8.如图，已知(4,0),(0,4)AB，从点(

15、2,0)P射出的光线经直线AB 反射后再射到直线OB 上，最后经直线OB 反射后又回到P 点，则光线经过的路程是。9.将一张坐标纸折叠一次，使得点(0,2)与点(4,0)重合，点(7,3)与点(,)m n重合，则mn。文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ

16、4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L

17、8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ

18、4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L

19、8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ

20、4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L

21、8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G14 BCOBAyPCxE直线夹角问题10.如图，已知等腰三角形ABC 中，ABAC，AB 边所在直线的方程为760 xy，AC 边所在直线的方

22、程为70 xy，底边 BC 所在直线通过点(3,8)P，求 BC 边所在的直线方程。11.已知ABC的顶点(3,1)A，过 B 点的内角平分线方程是41 00 xy，过 C 点的中线方程是610590 xy求顶点 B 的坐标和BC 边的方程。F有关距离问题12.求点(1,2)P到下列直线的距离：（1）2100 xy（2）32x13.求两平行线1:3410lxy和2:6830lxy间的距离。（公式法：两方程,x y的系数相等原点辅助法：注意两平行线在原点同侧还是两侧）14.过点(1,2)P引直线，使(2,3),(4,5)AB到它的距离相等，则这条直线的方程是。15.已知原点到过(1,3)P的直线

23、l的距离为1，求直线l的方程。16.点(,)P x y在直线:10lxy上运动，求224613xyxy的最小值。（配方法；几何意义法）G直线系17.求证：动直线222(23)(1)310mmxmmym恒过定点，并求出此定点坐标。18.曲线123xy与直线2yxm有两个交点，则m的取值范围是。四、平面区域A二元一次不等式表示的平面区域平面内一条直线:0lAxByC将平面分成三个部分，即直线l的两侧及直线上的点集，它们构成不同的区域。0AxByC区域：直线右上或右下0AxByC区域：直线左上或左下文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L

24、8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ

25、4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L

26、8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ

27、4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L

28、8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ

29、4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L

30、8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G15 B画平面区域问题1.画出不等式组326010440 xyxyxy所表示的平面区域。2.画出不等式(21)(3)0 xyxy表示的平面区域。3.画出不等式1xy所表示的平面区域。C不等式组所表示的平面区域的面积4.求不等式211xy所表示的平面区域的面积。5.求不等式组03434xxyxy所表示的平面区域的面积。6.若不等式组03434xxyxy所表示的平面区域被直线43ykx分为面积相等的两部分，则k的值是多少？D目标函数的最值问题7.若实数,x y满足

31、1002xyxy，则yx的取值范围是。8.已知,x y满足0024010 xyxyxy，则22(2)xy的最小值是。9.设,x y满足约束条件00134xyxyaa，若231xyzx的最小值为32，则a的值为。文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q

32、5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y

33、3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q

34、5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y

35、3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q

36、5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1文档编码:CD5I3L8D4Y3 HC6H3I6A2M6 ZJ4K7Q5Z7G1