如图,O为数轴的原点,在数轴上A点表示的数为a,B点表示的数为b,C点表示的数为c,b是最大的负整数,且
,
.点P从点B出发以每秒2个单位长度的速度向左运动,到达点A后立刻返回运动到点C并停止.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/30/57481825-38d9-48d9-ae3b-52fad36cceda.jpg?resizew=221)
(1)
________,
________,
________;
(2)点P从点B离开后,在点P到达点C的过程中,经过x秒钟,
,求x的值.
(3)点P从点B出发的同时,数轴上的点M,N分别点A和点C同时发相向而行,速度分别为每秒3个单位长度和每秒4个单位长度,假设运动t秒钟时,P、M、N三点中恰好有一个点是另外两个点的中点,请求出所有满足条件的t的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b1bfeb92e3df276961d605a6a2bd203.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e2e99816b67f125835e7cd4ea95aebe.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/30/57481825-38d9-48d9-ae3b-52fad36cceda.jpg?resizew=221)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccd4162c7d09f970cb77cadacdbe521.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4e9bb42376c12d7d21702ae8062b25a.png)
(2)点P从点B离开后,在点P到达点C的过程中,经过x秒钟,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b406c384b13fc95fb76c6833c88cddd1.png)
(3)点P从点B出发的同时,数轴上的点M,N分别点A和点C同时发相向而行,速度分别为每秒3个单位长度和每秒4个单位长度,假设运动t秒钟时,P、M、N三点中恰好有一个点是另外两个点的中点,请求出所有满足条件的t的值.
更新时间:2024-01-30 10:08:00
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相似题推荐
解答题-问答题
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【推荐1】已知点
在数轴上对应的数为
,点
在数轴上对应的数为
,且
,
之间的距离记为
或
,请回答问题:
(1)直接写出
的值,
______,
______,
______.
(2)设点
在数轴上对应的数为
,若
,则
______.
(3)如图,点
是数轴上的三点,点
表示的数为4,点
表示的数为
,动点
表示的数为
.
①若点
在点
之间,则
______;
②若
,则
______;
③若点
表示的数是
,现在有一蚂蚁从点
出发,以每秒1个单位长度的速度向右运动,当经过多少秒时,蚂蚁所在的点到点
、点
的距离之和是10?
![](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/b59d7d88c6e9b44cd8f824755be207d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2afd4acb164aad6d5a73989f5412730b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1103ddae6ffaba2b15808c6df09c0248.png)
(1)直接写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ee41430c643ad8b1241b6f161dc24a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccd4162c7d09f970cb77cadacdbe521.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c26a46e7879436d532af3f4b6e258a81.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/065e3a1e05535ca1843254490e602c44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
(3)如图,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b48386aac017c768709a87cda4b7001b.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/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/20/05ca8c81-8bf4-40a5-b7d0-9ac848797768.png?resizew=386)
①若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6670479a0083dd2dfd5ad55b47b1ab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e093018d5ac8c8bee584b70c4fd8c629.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a4f08df1be8c8ef14d7f76d300dc69d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
③若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d13ce3ebd1112220c639562739f1f9d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
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【推荐2】如图,数轴上每相邻两点相距一个单位长度,点A、B、C、D是这些点中的四个,且对应的位置如图所示,它们对应的数分别是a、b、c、d.
![](https://img.xkw.com/dksih/QBM/2020/4/6/2435636422647808/2436270124384256/STEM/c7bcd9cf3187491e8c39dec2a4e10539.png?resizew=369)
(1)若c与d互为相反数,则a________;
(2)若d2b8,那么点C对应的数是________;
(3)若abcd0,ab0求
的取值范围.
![](https://img.xkw.com/dksih/QBM/2020/4/6/2435636422647808/2436270124384256/STEM/c7bcd9cf3187491e8c39dec2a4e10539.png?resizew=369)
(1)若c与d互为相反数,则a________;
(2)若d2b8,那么点C对应的数是________;
(3)若abcd0,ab0求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/708bf739af58cb889177eabf8cc75b60.png)
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【推荐3】一个点A表示的数是a,点A在数轴上先向右移动2个单位长度,再向左移动3个单位长度,可以到达点B,点B表示的数为b,A、B间的距离可以表示为|AB|=|a-b|,
(1)如果点A表示数-3,将点A向右移动7个单位长度,那么终点B表示的数是_________;如果点A表示数是3,将点A向左移动7个单位长度,再向右移动5个单位长度,那么终点B表示的数是_______,一般地,如果点A表示数为a,将点A向右移动b个单位长度,再向左移动c个单位长度,那么请你猜想终点B表示的数是______________,A、B两点间的距离_____________.
(2)如果点A表示数为a,点B表示的数是-3,A、B两点间的距离是|AB|=2,则a的值为_____________.
(3)找出所有符合条件的整数a,使得|a+3|+|a-2|取得最小值,这样的整数是_____,最小值为_________.
(1)如果点A表示数-3,将点A向右移动7个单位长度,那么终点B表示的数是_________;如果点A表示数是3,将点A向左移动7个单位长度,再向右移动5个单位长度,那么终点B表示的数是_______,一般地,如果点A表示数为a,将点A向右移动b个单位长度,再向左移动c个单位长度,那么请你猜想终点B表示的数是______________,A、B两点间的距离_____________.
(2)如果点A表示数为a,点B表示的数是-3,A、B两点间的距离是|AB|=2,则a的值为_____________.
(3)找出所有符合条件的整数a,使得|a+3|+|a-2|取得最小值,这样的整数是_____,最小值为_________.
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【推荐1】已知数轴上的点
,
,
,
所表示的数分别是
,
,
,
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a438feb92bc9fab63843573a94631f14.png)
(1)则
______,
______;若点
,
沿数轴同时出发相向匀速运动,
秒后两点相遇,点
的速度为每秒
个单位长度,点
的运动速度为每秒______个单位长度;
(2)
,
两点以(
)中的速度从起始位置同时出发,向数轴正方向运动,与此同时,
点以每秒
个单位长度的速度向数轴正方向开始运动,在
秒时有
,求
的值;
(3)
,
两点以(
)中的速度从起始位置同时出发相向匀速运动,当点
运动到点
起始位置时,迅速以原来速度的
倍返回;到达出发点后,保持改后的速度又折返向点
起始位置方向运动;当点
运动到点
起始位置时马上停止运动,当点
停止运动时,点
也停止运动,在此运动过程中,
,
两点相遇,求点
,
相遇时在数轴上对应的数(请直接写出答案).
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95e35f76e01c3979ae5987f7729f9856.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3304e23f3b0f9569c4140ca89b6498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a438feb92bc9fab63843573a94631f14.png)
(1)则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4e9bb42376c12d7d21702ae8062b25a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5991e9ec7666f533a528a4173c58f0ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d48e9deca35c034db4734cf9d2ddf90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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【推荐2】已知数轴上有A、B两点,分别用
、
表示,且关于
、
的多项式
为三次单项式.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/d2452ab6-855d-4d6f-b80f-78c98753b831.png?resizew=385)
(1)求出
、
的值,并在数轴上标注A、B两点;
(2)若动点
从
点出发,以每秒2个单位长度的速度向左运动;同时动点
从A点出发,以每秒3个单位长度的速度向右运动,动点
到达原点后立即向左运动(只改变方向,不改变速度大小),则经过多长时间动点
与动点
到原点的距离相等;
(3)在(2)的条件下,
、
出发的同时,又有一动点
从
点出发,以每秒
个单位长度的速度向左运动,则经过多长时间,动点
、
、
互为余下两点的中点?(请直接写出答案)
![](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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/457ee55c8fd55c8282609bd8109f5b5a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/d2452ab6-855d-4d6f-b80f-78c98753b831.png?resizew=385)
(1)求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)若动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(3)在(2)的条件下,
![](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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22d3bf727f6c78896544c7f6c8ff33ba.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/ac047e91852b91af639feec23a9598b2.png)
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【推荐3】如图,在数轴上点
表示的数为
,点
表示的数为40,动点
从点
出发以每秒5个单位的速度沿正方向运动,动点
从原点出发以每秒4个单位的速度沿正方向运动,动点
从点
出发以每秒8个单位的 速度先沿负方向运动,到达原点后立即按原速返回,三点同时出发,当点
回到点
时,三点停止运动.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/acf89f48-e006-41c2-a85f-c78cd223c175.png?resizew=242)
(1)当运动时间为3秒时,点
、点
之间的距离是________单位.
(2)当
个单位时,求三个点的运动时间.
(3)尝试借助上面数学问题的解题经验,建立数轴完成下面的实际问题:
码头
位于
,
两码头之间,且知
海里,
海里,甲船从
码头顺流驶向
码头,乙船从
码头顺流驶向
码头,丙船从
码头开往
码头后立即调头返回
码头.已知甲船在静水中的航速为5海里/时,乙船在静水中的航速为4海里/时,丙船在静水中的航速为8海里/时,水流速度为2海里/时,三船同时出发,每艘船都行驶到
码头停止.在整个运动过程中,是否存在某一时刻,这三艘船中的一艘恰好在另外两船之间,且与两船的距离相等?若存在,请求出此时甲船离
码头的距离;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79ef63ad7b61f3fae0ac81148e7700ff.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/acf89f48-e006-41c2-a85f-c78cd223c175.png?resizew=242)
(1)当运动时间为3秒时,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dff7ba0385cda327f43ad12eba24ef30.png)
(3)尝试借助上面数学问题的解题经验,建立数轴完成下面的实际问题:
码头
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/cd0566be94b1ed3e5d250ca530eeb529.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25a3debb802dd4f3e774b16ad1c154ce.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
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【推荐1】已知
,
两点在数轴上分别表示有理数
,
,
,
两点之间的距离表示
,则A,
两点之间的距离
.数轴上
,
两点对应的数分别为
,
,
为数轴上一动点,且表示的数为
.
(1)A,
两点之间的距离是___________;
(2)①点
与表示
的点之间的距离为___________,
②若点
到
,B两点的距离相等,则点
表示的数为___________,
③若点
到
,B两点的距离之和为
,则点
表示的数为___________;
(3)现在点
以
个单位长度/秒的速度向右运动,同时点
以
个单位长度/秒的速度向右运动,当点
与点
之间的距离是
个单位长度时,直接写出点
所表示的数___________.
![](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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2afd4acb164aad6d5a73989f5412730b.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/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)A,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)①点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3edbd40e04e2a943051fa83d6e511add.png)
②若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
③若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](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/dad2a36927223bd70f426ba06aea4b45.png)
(3)现在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ec818fc0754296163206e1e8870f9e6.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/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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【推荐2】数轴上两点间的距离等于这两点所对应的数的差的绝对值.例:如图所示,点A、B在数轴上分别对应的数为a、b,则A、B两点间的距离表示为
.根据以上知识解题:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/18/699984d9-8eb1-4d35-9b8c-fc159ec9912b.png?resizew=217)
(1)若数轴上两点A、B表示的数为-2、3,则|AB|=____________;
(2)若数轴上两点A、B表示的数为x、-1,
①A、B之间的距离可用含x的式子表示为____________;
②若该两点之间的距离为2,那么x值为____________;
(3)|x+1|+|x-2|的最小值为___________.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b60a6e9515c220c8554719e399ec47.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/18/699984d9-8eb1-4d35-9b8c-fc159ec9912b.png?resizew=217)
(1)若数轴上两点A、B表示的数为-2、3,则|AB|=____________;
(2)若数轴上两点A、B表示的数为x、-1,
①A、B之间的距离可用含x的式子表示为____________;
②若该两点之间的距离为2,那么x值为____________;
(3)|x+1|+|x-2|的最小值为___________.
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【推荐1】【了解概念】
在平面直角坐标系
中,若
,式子
的值就叫做线段
的“勾股距”,记作
.同时,我们把两边的“勾股距”之和等于第三边的“勾股距”的三角形叫做“等距三角形”.
【理解运用】
在平面直角坐标系
中,
.
(1)线段
的“勾股距”
;
(2)若点
在第三象限,且
,求
并判断
是否为“等距三角形”﹔
【拓展提升】
(3)若点
在
轴上,
是“等距三角形”,请直接写出
的取值范围.
在平面直角坐标系
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/149a674889feb21c14b0b2e2a283e2fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e92b7cab23a22000baea1a2f30856e22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9edc12050866726580861db88862a12a.png)
【理解运用】
在平面直角坐标系
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bba1d73de6b8b2b519d9a03eb8c54a71.png)
(1)线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e61b64516bed9dabdd2980d9182101db.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d22132460960ac215b92dd6a972693b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e4c9f434258ad9710ffd213daa086ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
【拓展提升】
(3)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caa4915684d5762408c15f778fde5d10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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名校
【推荐2】已知数轴上两点A,B对应的数分别为a,b,点M为数轴上一动点,其中a,b满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3002357a952c2b5f63f1704dc5f3bfc.png)
(1)写出点A表示的数是 ;点B表示的数是 .
(2)若点M到A的距离是点M到B的距离的两倍,我们就称点M是[A,B]的好点.
①若点M到运动到原点O时,此时点M [A,B]的好点(填是或者不是)
②若点M以每秒1个单位的速度从原点O开始运动,当M是[A,B]的好点时,求点M所表示的数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3002357a952c2b5f63f1704dc5f3bfc.png)
(1)写出点A表示的数是 ;点B表示的数是 .
(2)若点M到A的距离是点M到B的距离的两倍,我们就称点M是[A,B]的好点.
①若点M到运动到原点O时,此时点M [A,B]的好点(填是或者不是)
②若点M以每秒1个单位的速度从原点O开始运动,当M是[A,B]的好点时,求点M所表示的数.
![](https://img.xkw.com/dksih/QBM/2020/10/14/2570726994083840/2572726640279552/STEM/8d7827b083154a678bca43cbbc0dbacb.png?resizew=395)
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【推荐3】阅读下列材料:
我们知道|x|的几何意义是在数轴上数x对应的点与原点的距离;即
,这个结论可以推广为
表示在数轴上数
对应点之间的距离;在解题过程中,我们经常会应用绝对值的几何意义来帮助我们分析问题.
例如在解含有绝对值的方程
时,我们可以利用绝对值的几何意义把问题理解成在数轴上找一点到2的距离等于1,如图1所示,显然这样的点有2个,对应的数分别为1,3,即原方程的解为
或
;并且我们还可以把图中阴影部分理解成到2的距离大于1的点在数轴上所对应的取值范围,即不等式
的解可表示为
或
;同样的,我们可以利用绝对值的几何意义把解方程
的过程理解成在数轴上找到一点使它与
和2的距离之和为5.
![](https://img.xkw.com/dksih/QBM/2024/2/2/3424639732064256/3438000892583936/STEM/4113dbd314e3429593ae3b023a66956a.png?resizew=550)
(1)参考以上阅读材料,回答下列问题:
①求出方程
的解为 ;
②若
,则m的取值范围可表示为;
(2)现给出如下定义:对于数轴上的任意点P、Q,若点P到点Q的距离为d(
),则称d为点P到点Q的追随值,记作
.例如,在数轴上点P表示的数是2,点Q表示的数是
,则点P到点Q的追随值为
.如图,点C表示的数是1,在数轴上有两个动点A、B都沿着正方向同时移动,其中A点的速度为每秒3个单位,B点的速度为每秒1个单位,点A从点C出发,点B从点D出发,点D表示的数是n,设运动时间为t(t>0).
![](https://img.xkw.com/dksih/QBM/2024/2/2/3424639732064256/3438000892583936/STEM/abbc96a3995847328423b675bcf19f16.png?resizew=374)
①当
时,问t为何值时,点A到点B的追随值
;
②若
时,点A到点B的追随值
,求n的取值范围.
我们知道|x|的几何意义是在数轴上数x对应的点与原点的距离;即
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec806110718f658b220663d35061060d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc6abf3f9b0ebcdc47a028c781b7edb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bff60eab72de85437e12806474281612.png)
例如在解含有绝对值的方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c47e517a8a2c73a5bb07e1ac820d3dbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55aa0a20848c37c1892c567b2315e04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ad81b25ca721ce7b1226e00c127f7e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/752455799e49f846e2601304fec5d3b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ccaa6e503b61e9ae78d8439cba2e328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/617aaad1fac4a6b2532c59c8c6e8d218.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://img.xkw.com/dksih/QBM/2024/2/2/3424639732064256/3438000892583936/STEM/4113dbd314e3429593ae3b023a66956a.png?resizew=550)
(1)参考以上阅读材料,回答下列问题:
①求出方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acae52f8e1260171b3eed5e03322bc.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48ee89f80e02d6e1682862ca270d3df7.png)
(2)现给出如下定义:对于数轴上的任意点P、Q,若点P到点Q的距离为d(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f8e68eb4ade6e22982d2df5102d8894.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa9ed163a70320ae5af9916c50d9656.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d13ce3ebd1112220c639562739f1f9d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87e771bc57fb6d6e2017afd3d4631ad7.png)
![](https://img.xkw.com/dksih/QBM/2024/2/2/3424639732064256/3438000892583936/STEM/abbc96a3995847328423b675bcf19f16.png?resizew=374)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fac3649308b528fd56545ba102dc42d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/702b487060aa24b45040cbc48f8b1caf.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a9651ef497f8bd97926c87cbef23392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/982dbb3b32390fe2ef440d2b15f07f55.png)
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