【概念与发现】
当点C在线段AB上,
时,我们称n为点C在线段AB上的“点值”,记作
.
例如,点C是AB的中点时,即
,则
;
反之,当
时,则有
.
因此,我们可以这样理解:“
”与“
”具有相同的含义.
(1)【理解与应用】
如图,点C在线段AB上.若
,
,则
________;若
,则
________.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/7/f9359afc-5e91-4464-a3bc-3f46edc9a506.png?resizew=162)
(2)【拓展与延伸】
已知线段
,点P以1cm/s的速度从点A出发,向点B运动.同时,点Q以3cm/s的速度从点B出发,先向点A方向运动,到达点A后立即按原速向点B方向返回.当P,Q其中一点先到达终点时,两点均停止运动.设运动时间为t(单位:s).
①小王同学发现,当点Q从点B向点A方向运动时,
的值是个定值,求m的值;
②t为何值时,
.
当点C在线段AB上,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c86948ba5afe6bbff880d801700e300c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/812c20fc9178d64ed224987a9c925b45.png)
例如,点C是AB的中点时,即
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd1fe7660ee42b8d3a9c076b700ae59a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e36adfd9469c23b5c1a0122260e97df5.png)
反之,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e36adfd9469c23b5c1a0122260e97df5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd1fe7660ee42b8d3a9c076b700ae59a.png)
因此,我们可以这样理解:“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/812c20fc9178d64ed224987a9c925b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c86948ba5afe6bbff880d801700e300c.png)
(1)【理解与应用】
如图,点C在线段AB上.若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d70dc2c20619a4fc12a0cfda59af5b69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42f706f43d112763184451c25bd3eaa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5502267166948b82c17a1bdabc61a78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43e1b1bc948dc2e9fcdd87f433087c08.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/7/f9359afc-5e91-4464-a3bc-3f46edc9a506.png?resizew=162)
(2)【拓展与延伸】
已知线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1cd4a1c8087ef697d82b321a3331211.png)
①小王同学发现,当点Q从点B向点A方向运动时,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a67dd2c0fd798c9addf3d64f84de4e7.png)
②t为何值时,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df3d1fb2c19f1ae8c0af0abdcf2eff51.png)
22-23七年级上·福建泉州·期末 查看更多[9]
福建省泉州实验中学2022-2023学年七年级上学期期末考试数学试卷福建省莆田市荔城区莆田第九中学2023-2024学年七年级上学期月考数学试题(已下线)专题11 线段上的动点与几何图形动角的探究问题之六大题型-【好题汇编】备战2023-2024学年七年级数学上学期期末真题分类汇编(人教版)(已下线)猜想05 与数轴、线段、角有关的复杂应用题(解答60题专练)-2023-2024学年七年级数学上学期期末考点大串讲(人教版)(已下线)专题4.8 线段中的四种常见思想方法-2023-2024学年七年级数学上册举一反三系列(人教版)(已下线)专题4.8 线段中的四种常见思想方法-2023-2024学年七年级数学上册举一反三系列(北师大版)(已下线)专题6.8 线段中的四种常见思想方法-2023-2024学年七年级数学上册举一反三系列(苏科版)(已下线)专题6.8 线段中的四种常见思想方法-2023-2024学年七年级数学上册举一反三系列(浙教版)(已下线)专题4.8 线段中的四种常见思想方法-2023-2024学年七年级数学上册举一反三系列(沪科版)
更新时间:2023-02-17 22:00:45
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解答题-问答题
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较难
(0.4)
【推荐1】如图,在平面直角坐标系中,长方形
的边
轴,点
的坐标为
,点
的坐标为
.点
从点
出发,以每秒3个单位长度的速度按顺时针方向,沿
运动,点
从点
出发,以每秒2个单位长度的速度按逆时针方向,沿
运动,当点
与点
相遇时运动停止.点
与点
同时出发,设点
与点
运动的时间为
,三角形
的面积为
.
(1)点
的坐标为______________,点
的坐标为______________;
(2)求点
与点
相遇处的坐标;
(3)用含
的式子表示
,并直接写出
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f4c57da0931466032ff40ec449650ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f528e7fda6cee97ee3a15c4f1ed5d7ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d483dd3a65702ed0cd7df766300d03b3.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/92f602a637e57761b115810931ae8e89.png)
![](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/d9853c90ab11d8bf821168accaffb8c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.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/2c1a48b92c61d209d0556e4cd8fdb70b.png)
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![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/25/df0ec7f4-1c24-471c-b861-945b713d1722.png?resizew=200)
(1)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(3)用含
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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解答题-问答题
|
较难
(0.4)
【推荐2】如图,已知数轴上
、
两定点对应的数是-
,
,动点
、
同时从点
出发向点
运动,到达点
后折返向点
继续运动,其中某点回到点
时,全部停止.(点
的速度为
个单位长度
秒,点
的速度为
个单位长度
秒)
(1)在点
到达
点前,
①经过______秒
、
之间间隔
个单位长度:
②经过______秒原点刚好位于
、
的最中间;
③经过______秒点
到点
的距离刚好等于点
到点
的距离(即
);
(2)当动点
到达点
后,点
开始改变速度以
个单位长度
秒的速度继续运动,
秒后,
、
两点之间相距
个单位长度,求
的值.
![](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/f179a5e46197a7f5f5646fefd47c1989.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
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(1)在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
①经过______秒
![](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/6f8c4c029e552954bd493b49aeab82d5.png)
②经过______秒原点刚好位于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
③经过______秒点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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(2)当动点
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【推荐1】如图,点C,D,E在线段
上,线段
,C是线段
上靠近点A的三等分点.点E为线段
的中点,且图中所有线段的长度和是线段
的长度的10倍,求
的长度.
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【推荐2】已知线段AB=12,CD=6,线段CD在直线AB上运动(A在B的左侧,C在D的左侧).
(1)当D点与B点重合时,AC=_________;
(2)点P是线段AB延长线上任意一点,在(1)的条件下,求PA+PB–2PC的值;
(3)M、N分别是AC、BD的中点,当BC=4时,求MN的长.
(1)当D点与B点重合时,AC=_________;
(2)点P是线段AB延长线上任意一点,在(1)的条件下,求PA+PB–2PC的值;
(3)M、N分别是AC、BD的中点,当BC=4时,求MN的长.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/14/364127b5-f355-49f7-9483-75de7665dd99.png?resizew=286)
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