1 . 在平面直角坐标系中,已知点
和点
,且满足
.
为不等式
的最大整数解,求
的值并判断点
在第几象限;
(2)在(1)的条件下,求
的面积;
(3)在(2)的条件下,若两个动点
,
,请你探索是否存在以两个动点
、
为端点的线段
,且
,若存在,求
、
两点的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65520f6d80caffaf45a37cb04cb21b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e64da29e0066e985f1971f5b9d820089.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2be513595f3e53ffefaef90ec5e268bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba13991195603903b44f45c8f3d31920.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)在(1)的条件下,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
(3)在(2)的条件下,若两个动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/906dea47e715132352660ddc78a4c10a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aba2ca965aac6b657172f5c9afd8cfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31307b00524e461b0ad8dfbcdf24bacf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f537e7bd7742eb543279795b98e83157.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
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2 . 【问题背景】盐丰快速通道是盐丰一体化发展的重要一环也是盐城市建设长三角一体化产业发展基地的“轴线”,被列为全市重点道路交通项目,一直是众人关注的焦点.
如图1,两辆盐丰公交P、Q在长9公里的
上同时相向匀速运动,盐丰公交P从A出发,速度为2公里/分钟,盐丰公交Q从B出发,速度为1公里/分钟,当盐丰公交P到达B时,盐丰公交P,Q停止运动.经过几分钟P,Q之间相距3公里?
【问题解决】小丰同学在学习《有理数》之后,发现运用数形结合的方法建立数轴可以较快地解决上述问题:如图2,将点A与数轴的原点O重合,点B落在正半轴上.设运动的时间为t(
).
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/4/19278978-8bf1-4919-a178-63127477c478.png?resizew=450)
(1)t分钟后点P在数轴上对应的数是______;点Q对应的数是______;(用含t的代数式表示)
(2)我们知道,如果数轴上M,N两点分别对应数m,n,则
.试运用该方法求经过几分钟P,Q之间相距3公里?
(3)在
上有一个标记位置C,
,若盐丰公交P与标记位置C之间的距离为a,盐丰公交Q与B之间的距离为b.在运动过程中,是否存在某一时刻t,使得
?若存在,请求出运动的时间;若不存在,请说明理由.
如图1,两辆盐丰公交P、Q在长9公里的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
【问题解决】小丰同学在学习《有理数》之后,发现运用数形结合的方法建立数轴可以较快地解决上述问题:如图2,将点A与数轴的原点O重合,点B落在正半轴上.设运动的时间为t(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5cfb01fe55aba6b2c05fb42a970547.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/4/19278978-8bf1-4919-a178-63127477c478.png?resizew=450)
(1)t分钟后点P在数轴上对应的数是______;点Q对应的数是______;(用含t的代数式表示)
(2)我们知道,如果数轴上M,N两点分别对应数m,n,则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0fe991abfc88cdb6c8d61521cada3a4.png)
(3)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d70dc2c20619a4fc12a0cfda59af5b69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a7dbc702617c765a573961953cc0901.png)
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名校
3 . “幸福是奋斗出来的”,在数轴上,若F到A的距离刚好是3,则F点叫做A的“幸福点”;若F到A、B的距离之和为6,则F叫做A和B的“幸福中心”.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/4/63ce5a1b-b263-4851-a9af-c7836353d092.png?resizew=387)
(1)若点A表示的数为
,则A的幸福点F所表示的数应该是________;
(2)如图1,M、N为数轴上两点,点M所表示的数为4,点N所表示的数为
,若点F就是M和N的幸福中心,则F所表示的所有数中,整数之和为________;
(3)如图2, A、B、C为数轴上三点,点A所表示的数为
,点B所表示的数为4,点C所表示的数为8.
①若点P,Q分别从点A,B以每秒2个单位长度的速度向右运动,点R从点C出发,以每秒3个单位长度的速度向左运动,经过________秒时,点R是P和Q的幸福中心;
②若点P从点A以每秒2个单位长度的速度向左运动,点Q、R分别从点B、C以每秒3个单位长度和每秒4个单位长度的速度向右运动,是否存在常数m,使得
为定值?若存在,请求出m值以及这个定值;若不存在,请说明理由.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/4/63ce5a1b-b263-4851-a9af-c7836353d092.png?resizew=387)
(1)若点A表示的数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
(2)如图1,M、N为数轴上两点,点M所表示的数为4,点N所表示的数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
(3)如图2, A、B、C为数轴上三点,点A所表示的数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
①若点P,Q分别从点A,B以每秒2个单位长度的速度向右运动,点R从点C出发,以每秒3个单位长度的速度向左运动,经过________秒时,点R是P和Q的幸福中心;
②若点P从点A以每秒2个单位长度的速度向左运动,点Q、R分别从点B、C以每秒3个单位长度和每秒4个单位长度的速度向右运动,是否存在常数m,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65a546aea22f3fbc0b6d621e664e1090.png)
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2023-12-01更新
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210次组卷
|
3卷引用:广东省 广州市第二中学2023-2024学年七年级上学期期中数学试题
广东省 广州市第二中学2023-2024学年七年级上学期期中数学试题(已下线)七年级数学期末模拟卷02(江西专用)(人教版七上全册)-学易金卷:2023-2024学年初中上学期期末模拟考试江苏省宿迁市宿城区苏州外国语实验学校2023-2024学年七年级上学期12月月考数学试题
23-24七年级上·江苏·周测
名校
4 . 数轴是一个非常重要的数学工具,它把数和数轴上的点建立了对应关系, 形象地揭示了数与数轴上的点之间的内在联系,是数形结合的基础.小明在一条长方形纸带上画了一条数轴,进行如下操作探究:
(1)操作1:折叠纸带,使数轴上表示3的点与表示
的点重合,则表示数
的点与表示数 的点重合,表示数
的点与表示数 (用含a 的式子表示)的点重合;
(2)操作2:在计算满足
的x的值时,也可以通过折叠数轴的方法来解决:先在数轴上取表示
的点,然后沿着该点折叠数轴,最后找到距离该点3个单位长度的点,读取数据得 ;利用该方法求出满足
的x的取值范围为 ;
(3)操作3:在数轴上A 、B 两点对应的数分别为
、20,数轴上一点C 对应的数为x,数 轴上一点D 与点C 始终保持18个单位长度(点D 位于点C 的左侧).折叠数轴,使得 C、D 重合,且折叠后A 、B 两点之间的距离为10,求出x 的值.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/23/8bb52f61-30e9-4d50-8526-6f94b4ac27b1.png?resizew=275)
(1)操作1:折叠纸带,使数轴上表示3的点与表示
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01317332a203c898536b1d0459f51d23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/008e77135f850cd4beab452480a591d6.png)
(2)操作2:在计算满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23141e8cd7ae578e5cf7cccc01097f72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c5ea90581a6073cd279694b17832fa.png)
(3)操作3:在数轴上A 、B 两点对应的数分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ab66291ef17f0d1664cefd6f6bffd31.png)
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5 . 在数轴上,点M和N分别表示数m,n,可以用绝对值表示点M,N两点间距离d
,即
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/26/32252e68-f516-4541-8d26-069d3a211b89.png?resizew=223)
(1)在数轴上,点A,B,C,D分别表示数
,7,x,y,解决以下问题:
①
_____;
②若
,则
_____;
③若
,求y的值.
(2)在数轴上,点A,B分别表示数a,b,点E是数轴上一点,满足
,请在数轴上表示出所有符合条件的点E.(在数轴上把选定区域用铅笔加粗,并标注必要的数据,用含a,b的代数式表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e092578f45dc0505c79fad83eb0d56db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aae24ef2d277d51bca43ec1667462eb6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/26/32252e68-f516-4541-8d26-069d3a211b89.png?resizew=223)
(1)在数轴上,点A,B,C,D分别表示数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81fb134b2b48acc99213fff6ccfee65f.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5267ff7ce5aa65879b770aa1990c0a7.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f28856087da9930c757d5a94af81e781.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/529bc60ac4b0bb65805c34414a0c0a61.png)
(2)在数轴上,点A,B分别表示数a,b,点E是数轴上一点,满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0f81f239eac588b43cd10c25e84d70b.png)
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2023-11-17更新
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237次组卷
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2卷引用:江苏省南京市鼓楼区2023-2024学年七年级上学期期中数学试题
6 . 数学实验室:
阅读下面材料,回答问题:已知点
、
在数轴上分别表示有理数
、
,
、
两点之间的距离表示为
.数轴上
、
两点的距离
,如数轴上表示
和
的两点之间的距离是5,利用上述结论,回答以下问题:
(1)数轴上表示2和6的两点之间的距离是____,数轴上表示1和
的两点之间的距离是_____;
(2)若表示数
和
的两点之间的距离是5,那么
________;
(3)若数轴上表示数
的点位于
与
之间,则
的值为________;
(4)若x表示一个有理数,且
,则有理数
的取值范围________;
(5)若未知数x,y满足
,求代数式
的最小值和最大值.
解:对于代数式
,数轴上,当
在
和
之间时,表示
的点到
与
的距离和最小,最小值为7,同理,对于
,数轴上,当
在
和
之间时,
到
和
的距离和最小,最小值为4,
又∵
,
∴ x的取值范围是________;y的取值范围是________.
∴
的最大值为________;
的最小值为________.
阅读下面材料,回答问题:已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2afd4acb164aad6d5a73989f5412730b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
(1)数轴上表示2和6的两点之间的距离是____,数轴上表示1和
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3edbd40e04e2a943051fa83d6e511add.png)
(2)若表示数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81fb134b2b48acc99213fff6ccfee65f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
(3)若数轴上表示数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3304e23f3b0f9569c4140ca89b6498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e58d0db5da495af8a86a70d9d0161ee2.png)
(4)若x表示一个有理数,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/088b6f827e9bdb722c1f3741b64189d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(5)若未知数x,y满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9f52ebcc9a4a81f1c1078257504134.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88584cf1df43e28d03592c7998b1653.png)
解:对于代数式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53e59970ce74dcbf5526e636c782eea1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d13ce3ebd1112220c639562739f1f9d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d13ce3ebd1112220c639562739f1f9d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a552fc359bbdae21d95cb9166a4bc81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81fb134b2b48acc99213fff6ccfee65f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81fb134b2b48acc99213fff6ccfee65f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
又∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddfa586cd4cddd466f7256a0c96364f5.png)
∴ x的取值范围是________;y的取值范围是________.
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88584cf1df43e28d03592c7998b1653.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88584cf1df43e28d03592c7998b1653.png)
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7 . 结合数轴与绝对值的知识回答下列问题:
(1)数轴上表示4和1的两点之间的距离是______;表示
和2两点之间的距离是______;一般地,数轴上表示数m和数n的两点之间的距离等于
.如果表示数a和
的两点之间的距离是3,那么
______
(2)若数轴上表示数a的点位于
与2之间,求
的值;
(3)利用数轴找出所有符合条件的整数点x,使得
,求所有符合条件整数点表示的数的和.
(4)解析当a为何值时
的值最小,并求出
的最小值.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/23/d7e56137-1b94-4c60-8b8c-25fa504c916d.jpg?resizew=253)
(1)数轴上表示4和1的两点之间的距离是______;表示
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81fb134b2b48acc99213fff6ccfee65f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae9dd56551121a5b88be4dc6910c9ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
(2)若数轴上表示数a的点位于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3edbd40e04e2a943051fa83d6e511add.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd0684e322e535e7756fea41eb2e6636.png)
(3)利用数轴找出所有符合条件的整数点x,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/631d4c7dfccb9a223eda83b8a0c22704.png)
(4)解析当a为何值时
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14cc389f7fa6e26914638cd2ae957a2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14cc389f7fa6e26914638cd2ae957a2f.png)
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8 . 如图,已知数轴上点
表示的数为
,
是数轴上位于点
左侧一点,且点
与点
的距离为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/10/89d6c52c-55d9-4e1b-809d-3bec65302104.png?resizew=163)
(1)写出数轴上点
表示的数__________;
(2)
表示
与
之差的绝对值,实际上也可理解为
与
两数在数轴上所对的两点之间的距离.
如
的几何意义是数轴上表示有理数
的点与表示有理数
的点之间的距离.试探索:
若
,则
__________;![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c650fe55b7603f106c53ca2423451c6.png)
的最小值为__________.
(3)动点
从
点出发,以每秒
个单位长度的速度沿数轴向右匀速运动,设运动时间为
秒,当
__________,点
,
两点之间的距离为
;
(4)动点
,
分别从
,
两点,同时出发,点
以每秒
个单位长度沿数轴匀速运动,
点以
个单位速度,沿数轴匀速运动,设运动时间为
秒.当
,
之间的距离为
时,则
的值为__________.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3304e23f3b0f9569c4140ca89b6498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49e60fbe6820130fb20abc555a94b5ea.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/10/89d6c52c-55d9-4e1b-809d-3bec65302104.png?resizew=163)
(1)写出数轴上点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4adb0fe30e6a27e2d212536fd76fafc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
如
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec2b0af17241d77dc875ce0ad97ef7a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e1c9ae241fd78126274c65e17990c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31562c66e57c5a0940ed3e8e2aaea4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c650fe55b7603f106c53ca2423451c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/678ca4f156bb4bea3cbcb577b522afa1.png)
(3)动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/825116eb345f5505ebc8c1cdb8a1f131.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
(4)动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecf4b43b6792b9ae78a1c8cae4e60524.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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9 . 如图,点A、B在数轴上分别表示有理数a、b,A、B两点之间的距离表示为
,在数轴上A、B两点之间的距离
.回答下列问题:
(1)数轴上表示2和5的两点之间的距离是_______,表示
和3的两点之间的距离是________.
(2)设点P在数轴上对应的数为x,若
,则
________.
(3)数轴上表示x和
的两点之间的距离为______________.
(4)当整数
_________________时,代数式
有最小值为________.
(5)当x取何值时,代数式
的值等于8 ?(写出过程)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87a25a5f6c65fd66ad1900774e2a1ac8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/31/10d32986-ad15-4dc9-a5b7-ec5b1d9f74b0.png?resizew=235)
(1)数轴上表示2和5的两点之间的距离是_______,表示
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
(2)设点P在数轴上对应的数为x,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4784ce39d25d5b2a2c9f3713e4abbd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
(3)数轴上表示x和
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
(4)当整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/232b9d0d7b7df068be770f5018cfd692.png)
(5)当x取何值时,代数式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/232b9d0d7b7df068be770f5018cfd692.png)
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10 . 点
、
在数轴上分别表示有理数
、
,则
、
两点之间的距离表示为
.如表示数
的点与表示数
的点的距离为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c61369309623cdf1521e6c19301de50.png)
利用数形结合思想回答下列问题:
如图,在数轴上有一根铁丝,铁丝的左端点
对应的数为
,右端点
对应的数为
.
(1)铁丝的长为_____.
(2)现将铁丝向右移动,此时点
对应的数为
,点
对应的数为
,
若铁丝向右移动1个单位长度,求
的值;
若
,请计算铁丝向右移动的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f82e415812cca9545611c0faa0c01b1c.png)
是否有最小值?如果有,请直接写出该最小值;如果没有,请说明原因.
(3)结论推广:数轴上有
、
、
三个数则
____
[填“
”、“
”、“
”(大于或等于)、或"
”(小于或等于)]
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a13880b9454c5942f164d934b1834783.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81fb134b2b48acc99213fff6ccfee65f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c61369309623cdf1521e6c19301de50.png)
利用数形结合思想回答下列问题:
如图,在数轴上有一根铁丝,铁丝的左端点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a94acdfb41489d5694b5a64b9e99754.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/26/b9402e8f-fdac-4cc0-9e4c-c4d203aed26d.png?resizew=469)
(1)铁丝的长为_____.
(2)现将铁丝向右移动,此时点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e1c9ae241fd78126274c65e17990c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed4bd51878a0eae716791cdfa4312bf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c650fe55b7603f106c53ca2423451c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c06f95ffce28a9a1850ca87552c51d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f82e415812cca9545611c0faa0c01b1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed4bd51878a0eae716791cdfa4312bf0.png)
(3)结论推广:数轴上有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e90d62a530477debeb8d53930018f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a13880b9454c5942f164d934b1834783.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/392cdb9d30684cce244bef94b8d861b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ff7942da6c3fc4005256fb1458557c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e119c508fd265e3e3d78749e54fe4f43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8536a5ebd76f494c03019086506d8e6a.png)
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