通过构造恰当的图形,可以对线段长度、图形面积大小等进行比较,直观地得到一些不等关系或最值,这是“数形结合”思想的典型应用.
【理解】
(1)如图1,
,垂足分别为C、D,E是
的中点,连接
.已知
,
.
①分别求线段
、
的长(用含a、b的代数式表示);
②比较大小:
__________
(填“<”、“=”或“>”),并用含a、b的代数式表示该大小关系.
![](https://img.xkw.com/dksih/QBM/2021/7/3/2756432937345024/2756441517473792/STEM/8fdff4ba-4a98-460e-b51d-647b9b42e9aa.png)
【应用】
(2)如图2,在平面直角坐标系
中,点M、N在反比例函数
的图像上,横坐标分别为m、n.设
,记
.
①当
时,
__________;当
时,
________;
②通过归纳猜想,可得l的最小值是__________.请利用图2构造恰当的图形,并说明你的猜想成立.
【理解】
(1)如图1,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca117bab387a262da24268b3def4e03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5228da61bed106b28849ef91a2ec116.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28d7c7183688014ca90f7241f176a99d.png)
①分别求线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
②比较大小:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/2021/7/3/2756432937345024/2756441517473792/STEM/8fdff4ba-4a98-460e-b51d-647b9b42e9aa.png)
【应用】
(2)如图2,在平面直角坐标系
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec549f15430d63c3dc6c6e94e7321ee5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c971221ef7683b12fb8a83438feeb8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d7185daae440233e6c38bbadd8e18b5.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e53b18b9dc6839a7b6c46b77641b06e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/050294162a78c6f4d6a87849bd3049a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2685cd527bc3f3b76315c8cf6ee7f2f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/050294162a78c6f4d6a87849bd3049a3.png)
②通过归纳猜想,可得l的最小值是__________.请利用图2构造恰当的图形,并说明你的猜想成立.
2021·江苏常州·中考真题 查看更多[10]
江苏省常州市2021年数学中考真题2022年山东省济宁市兖州区中考一模数学试题(已下线)专题33 阅读理解探究题压轴题-备战2022年中考数学临考题号押题(全国通用)2022年山东省青岛市九年级下学期第二次质量检测数学试题2022年山东省青岛第三十九中学九年级下学期二模数学试题2022年湖北省鄂州市梁子湖区中考模拟(二模)考试数学试题(已下线)专题10 反比例函数-三年(2020-2022)中考数学真题分项汇编(江苏专用)(已下线)2022年湖北省荆州市中考数学真题变式题21-24题山东省青岛市崂山区2022-2023学年九年级上学期期末数学试题2022年贵州省铜仁学院附中中考数学适应性试卷
更新时间:2021-07-03 20:17:32
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【推荐1】如图,在平面直角坐标系中,直线y=-3x+3与x轴,y轴分别交于A,B,两点,以AB为边在第一象限内作正方形ABCD,点D在反比例函数y=
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【推荐2】如图,在平面直角坐标系中,直线y=kx+n(n<0)与反比例函数y=
(m>0)的图象交于第一象限的点A,与x轴、y轴分别交于点B、C.
![](https://img.xkw.com/dksih/QBM/2021/8/6/2780100198916096/2781793196785664/STEM/1445bd96c2274d8db40105892dac0926.png?resizew=169)
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①直接填空:m的值为_______,k的值为_______;
②点P是x轴上一点,且位于点B的右侧.若△PAC的面积为6,求点P的坐标;
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f7626c207a4dc82d4d59cb520c91e49.png)
![](https://img.xkw.com/dksih/QBM/2021/8/6/2780100198916096/2781793196785664/STEM/1445bd96c2274d8db40105892dac0926.png?resizew=169)
(1)若n=﹣1,点A的坐标为(2,3).
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f7626c207a4dc82d4d59cb520c91e49.png)
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【推荐1】如图,
是
的外接圆,
为直径,
下方的半圆上找点D,使得
(保留作图痕迹,不写作法);
(2)在(1)所作的图中,连接
,
,
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①求四边形
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的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b997b0da1c9338e640206bfc0d0a427a.png)
(2)在(1)所作的图中,连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4630b9ca3d20635161fa8fbf812b9128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01571ba9e67d681d38907c8087ae6266.png)
①求四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c593ebdb2f1934a0cb56f8c44f454f8.png)
②求O到弦
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
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解答题-证明题
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较难
(0.4)
【推荐2】如图,
是
的高,
是
的中线,
,
,
,直线
交
于点M,交
于点N.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/24/73bf2568-d36c-4c50-b8c6-095482ea530e.png?resizew=162)
(1)求证:四边形
是平行四边形;
(2)求
的度数;
(3)当
,
时,求线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826c728050e3378921442ace20269ef6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59182f25fcf22afc79e28ded936de018.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/105068b25f5a63af32f4082cfe08691e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b41f2f95d643629321deb6e905c4f1ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826c728050e3378921442ace20269ef6.png)
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(1)求证:四边形
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(2)求
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(3)当
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