如图,在平面直角坐标系中,点
在
轴的正半轴上,点
在
轴的负半轴上,点
在
轴的正半轴上,且
,线段
、
的长是一元二次方程
的两个根,且
.
(1)求点
、点
、点
的坐标;
(2)若直线
过点
交线段
于点
,且
,求
点坐标;
(3)在平面内是否存在一点
,使得以
为直角顶点的
与
相似,若存在,请直接写出满足条件的点
的坐标;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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cb887ebce959b97ef37019ceebb653e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cf4b9e34f7fe11941e75bfc23702ece.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/26/e0c6d352-9b03-47d9-80ef-07b0e02f6e3d.png?resizew=196)
(1)求点
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/785ad8ecca6fd36a894f73579d4f7bc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(3)在平面内是否存在一点
![](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/9524e3810e06dc781285f1289e75d653.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
更新时间:2023-10-23 15:05:52
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【推荐1】小明是魔方爱好者,他擅长玩各种魔方,从二阶魔方到九阶魔方,他都能成功复原.有一天,小明突然想到一个问题,在九阶魔方中,到底含有多少个长方体呢?为此,我们先来解决这样一个数学问题:如图,图1是一个长、宽、高分别为a,b,c(a≥2,b≥2,c≥2,且a,b,c是正整数)的长方体,被分成了a×b×c个棱长为1的小立方体.这个几何体中一共包含多少个长方体(包括正方体)?(参考公式:1+2+3…+n
).
探究一:如图2,该几何体有1个小立方体组成,显然,该几何体共有1个长方体.如图3,该几何体有2个小立方体组成,那么它一共包含1+2=3个长方体.如图4,该几何体有3个小立方体组成,那么它一共包含 个长方体.如图5,该几何体﹣共包含210个长方体,那么该几何体共有 个小立方体组成.
探究二:如图6,该几何体有4个小立方体组成,那么它一共包含(1+2)×(1+2)=9个长方体.如图7,该几何体有6个小立方体组成,那么它一共包含 个长方体.如图8,该几何体共有2m个小立方体组成,那么该几何体一共有 个长方体.
探究三:如图1,该几何体共有个a×b×c小立方体组成,那么该几何体共有 个长方体.
探究四:我们现在可以解决小明开始的问题了.在九阶魔方(即a=b=c=9)中,含有 个长方体.
探究五:聪明的小明在学习了三种视图后,又提出一个新的问题:在图1中,若a=6,b=4,c=5,如果拿走一些小立方体后,剩下几何体的三种视图与原图1的三种视图完全一样,那么最多可以拿走 个小立方体;此时,剩下的几何体的表面积是 .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4878947f03747c13d62540fde471b985.png)
探究一:如图2,该几何体有1个小立方体组成,显然,该几何体共有1个长方体.如图3,该几何体有2个小立方体组成,那么它一共包含1+2=3个长方体.如图4,该几何体有3个小立方体组成,那么它一共包含 个长方体.如图5,该几何体﹣共包含210个长方体,那么该几何体共有 个小立方体组成.
探究二:如图6,该几何体有4个小立方体组成,那么它一共包含(1+2)×(1+2)=9个长方体.如图7,该几何体有6个小立方体组成,那么它一共包含 个长方体.如图8,该几何体共有2m个小立方体组成,那么该几何体一共有 个长方体.
探究三:如图1,该几何体共有个a×b×c小立方体组成,那么该几何体共有 个长方体.
探究四:我们现在可以解决小明开始的问题了.在九阶魔方(即a=b=c=9)中,含有 个长方体.
探究五:聪明的小明在学习了三种视图后,又提出一个新的问题:在图1中,若a=6,b=4,c=5,如果拿走一些小立方体后,剩下几何体的三种视图与原图1的三种视图完全一样,那么最多可以拿走 个小立方体;此时,剩下的几何体的表面积是 .
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【推荐2】如图,在平面直角坐标系中,
、
分别为
、
轴正半轴上的动点,
,若
和
的长分别是关于
的方程![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a705ed178fb63e4a7a025c27e6ae9e0.png)
的两个实数根.
![](https://img.xkw.com/dksih/QBM/2020/3/29/2436557523959808/2438313895895040/STEM/a9c6fd0c0ca6454092d0c552b9c1ac6a.png?resizew=167)
(1)求
的长;
(2)若
,求点
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4340375ca8abdbd6998760c944f38d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a705ed178fb63e4a7a025c27e6ae9e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b63f3bb2ea4acfb636aa9764b0211226.png)
![](https://img.xkw.com/dksih/QBM/2020/3/29/2436557523959808/2438313895895040/STEM/a9c6fd0c0ca6454092d0c552b9c1ac6a.png?resizew=167)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce7569721b330db1c3e703a8d660abe0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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【推荐1】如图1,在平面直角坐标系中,直线
与直线
交于点A,已知点A的横坐标为
,直线
与x轴交于点B,与y轴交于点C,直线
与x轴交于点F,与y轴交于点D.
![](https://img.xkw.com/dksih/QBM/2020/12/12/2619579670052864/2620618178322432/STEM/e60edb29-d16c-48bf-acbc-52d6aa3cc10f.png?resizew=742)
(1)求直线
的解析式;
(2)将直线
向上平移
个单位得到直线
,直线
与y轴交于点E,过点E作y轴的垂线
,若点M为垂线
上的一个动点,点N为
上的一个动点,求
的最小值;
(3)已知点
分别是直线
上的两个动点,连接
,是否存在点
,使得
是以点Q为直角顶点的等腰直角三角形,若存在,求点Q的坐标若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f84b4d320c54911ba365f4b8bc83b9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b60ca966e30bf50783a4f3d8dbc92e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/666f8546ddd14febfa3c57abbefbffcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://img.xkw.com/dksih/QBM/2020/12/12/2619579670052864/2620618178322432/STEM/e60edb29-d16c-48bf-acbc-52d6aa3cc10f.png?resizew=742)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
(2)将直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c0874f019492261eb175bdcc08c189d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9fce9427c9b17e4d3cda0c3ff3e2e14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9fce9427c9b17e4d3cda0c3ff3e2e14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f2813ee8f26cca880b6427f5f545d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f2813ee8f26cca880b6427f5f545d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0ae624767758791f9a10d33fc2d8bda.png)
(3)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5b1b15a4605fce993cb13aefbf40360.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50297ad9f7256b4d2efc3462289f18b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bd01207947515932c6f3704d18f628.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5b1b15a4605fce993cb13aefbf40360.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17277a306d4d0a0a0cf293f87802cf66.png)
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【推荐2】如图,一次函数
的图象与x、y轴分别相交于点A、B,四边形
是正方形.
![](https://img.xkw.com/dksih/QBM/2020/11/20/2596900463599616/2601390695022592/STEM/1510957d814849e3982fc1990f6f3919.png?resizew=137)
(1)求点A、B、C、D的坐标.
(2)设P是坐标轴上任意一点,若三角形
是以
为底边的等腰三角形,求P点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78b5062be5cf27ae8089ad0c25d1b7c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/2020/11/20/2596900463599616/2601390695022592/STEM/1510957d814849e3982fc1990f6f3919.png?resizew=137)
(1)求点A、B、C、D的坐标.
(2)设P是坐标轴上任意一点,若三角形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4d781525777c7b5284dffc70b2a28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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【推荐1】综合与实践
问题情境:数学活动课上,王老师出示了一个问题:如图1,在
中,
,D是
延长线上一点,连接
,
,点E在线段
上,且
,连接
.
求证
.
独立思考:(1)请解答王老师提出的问题.
实践探究:(2)在原有问题条件不变的情况下,王老师增加下面的条件,并提出新问题,请你解答.
“如图2,连接
,以B为圆心,
长为半径画弧,交
于点F,连接
,探究线段
与
之间的数量关系,并证明.”
问题解决:(3)数学活动小组对上述问题进行特殊化研究之后,提出下面的问题,请你解答.
“如图3,在(2)条件下,过E作
于K,若
,
,求
的长.”
问题情境:数学活动课上,王老师出示了一个问题:如图1,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a690535ef8766d108cce93b9e8544311.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0fa1aa5a7a5bb172ed4603f17c8b2c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffb4b6decc8aefd7371cd0b7afa56b2e.png)
独立思考:(1)请解答王老师提出的问题.
实践探究:(2)在原有问题条件不变的情况下,王老师增加下面的条件,并提出新问题,请你解答.
“如图2,连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
问题解决:(3)数学活动小组对上述问题进行特殊化研究之后,提出下面的问题,请你解答.
“如图3,在(2)条件下,过E作
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72a71b9b896f53c58aa26245d5854631.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/377b5f7197e5bd1afeea4d931307956a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b92be24459efab144c2ae9f8ddc14be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f64c372f6162c32675bfc005cffa6956.png)
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【推荐2】如图,在平行四边形
中,
的平分线交
于点
,交
的延长线于点
,以
,
为邻边作平行四边形
.
,如图
,求证:平行四边形
是正方形;
(2)若
,如图
,连接
,
,求证:
;
(3)若
,如图
,若
,
,
是
的中点,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22d7bc33b9ab8c8824bcae3366b1bf58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cdd9f345915ae742ed3dcd3f9678264.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9171484a68c84cad91e4f2233392f600.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8120f2eeb724c756b5f84a14c6df527.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/741f109c7c09317136588899ffcbd9c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d9e84e82d6ad85d631bbb3cb682c369.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307e785b90bb03f946e84f4c06e45d95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/741f109c7c09317136588899ffcbd9c6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aedf65d7d930fdb972d4802c0dea8b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e39adf871a542f06d911a891a75bab53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/999a995a6d07c561ce64e8952994160a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935ad59079c158ea0f92018fc548e4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08b0eb389bbe576cf8d7d346e2390f95.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d9e84e82d6ad85d631bbb3cb682c369.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afd056bf480a04dafb4b6da24662cc9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/377f5c10cf527c87ab06bff61384f7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df9a15966dde96392732e585e093b85b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0215e13a9fb5574d5194aeb9507a98aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ef9d0784478511736255074b9395fae.png)
您最近一年使用:0次
解答题-问答题
|
较难
(0.4)
【推荐1】如图,已知抛物线
与x轴交于A、
两点,与y轴交于
.
![](https://img.xkw.com/dksih/QBM/2022/12/28/3140801722220544/3144334060666880/STEM/21b9fc19040c452eb32a4a49c9e09d1f.png?resizew=179)
(1)求点A的坐标;
(2)点P在抛物线上,若
,求出点P的坐标;
(3)如图2,点D在线段
上,
直线
于点E,当
时,直接写出点D的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2299f88146e5a525b515a2ed36dfd1fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/316ba5cbb31299d683ac6c7dd795db85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f0ec7f84f716a316ec92d133927666c.png)
![](https://img.xkw.com/dksih/QBM/2022/12/28/3140801722220544/3144334060666880/STEM/21b9fc19040c452eb32a4a49c9e09d1f.png?resizew=179)
(1)求点A的坐标;
(2)点P在抛物线上,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef2eaeea340e51a3e4e331a200ca6731.png)
(3)如图2,点D在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/662698361c6b3ddaf0c28a3c87be53e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6cee57e535a20053e3ccec39e2c53a5.png)
您最近一年使用:0次
解答题-证明题
|
较难
(0.4)
真题
解题方法
【推荐2】如图,在菱形ABCD中,
,
,点E为边AB上一个动点,延长BA到点F,使
,且CF、DE相交于点G
![](https://img.xkw.com/dksih/QBM/2021/7/17/2766194709061632/2766937643384832/STEM/f4d66aa43e8e438fb3a091b011fe5143.png?resizew=531)
(1)当点E运动到AB中点时,证明:四边形DFEC是平行四边形;
(2)当
时,求AE的长;
(3)当点E从点A开始向右运动到点B时,求点G运动路径的长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea4f5eec0addba78f2e0cdfb7ecc59a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ac3d3b55561ec5d4acc242ecd1c7f41.png)
![](https://img.xkw.com/dksih/QBM/2021/7/17/2766194709061632/2766937643384832/STEM/f4d66aa43e8e438fb3a091b011fe5143.png?resizew=531)
(1)当点E运动到AB中点时,证明:四边形DFEC是平行四边形;
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6f6c04bc017ced739230d14ba31948.png)
(3)当点E从点A开始向右运动到点B时,求点G运动路径的长度.
您最近一年使用:0次
解答题-问答题
|
较难
(0.4)
【推荐3】已知矩形
中,
是对角线,
,
,点P为边
上的一个动点,动点P从点A出发沿
边向点D运动,速度是
,点Q为边C上的一个动点,动点Q从点C出发沿
边向点A运动,速度是
,
是过点Q的直线,分别交
、
于点E,F;且运动过程中始终保持
于点Q,P、Q两点同时出发,设运动时间为t秒,且
,解答下列问题:
![](https://img.xkw.com/dksih/QBM/2023/8/23/3309270070927360/3456517431582720/STEM/d1c7a07f74a0491f812b8e55712d5c0b.png?resizew=205)
(1)连接
,t为何值时,四边形
是平行四边形?
(2)连接
、
,设四边形
的面积为
,求y关于t的函数关系式;
(3)请从选择以下任意一题作答,我选 (若同时作答①和②,按①解答计分).
①连接
,是否存在某一时刻t,使点E在
平分线上时,求t的值,若不存在,请说明理由;
②是否存在某一时刻t,使点F在
垂直平分线上,若存在,求t的值,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b35ed92397da56c7afbd6967597a9611.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9547f6b5c7c54d216ecea72becb7d373.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5631e6ec24d3d67bf4592313b6b3f4f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abaeba15f3abdd877bc701af52c5cd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5631e6ec24d3d67bf4592313b6b3f4f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8de4a54cc7818be87a239f6de5f5d05b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d877aff07f8ac80e6dd5718b07f1a7f.png)
![](https://img.xkw.com/dksih/QBM/2023/8/23/3309270070927360/3456517431582720/STEM/d1c7a07f74a0491f812b8e55712d5c0b.png?resizew=205)
(1)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dd91fffd81d5ee507395f59eb9ddf59.png)
(2)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f541f7ae7c39082d202efd28805c54e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fce76109c3b574feaca9cd7029c2875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0033dcf0bc05bf877c412a7834d11a6b.png)
(3)请从选择以下任意一题作答,我选 (若同时作答①和②,按①解答计分).
①连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fbf1667b21a273bf5dd007d65eeda7c.png)
②是否存在某一时刻t,使点F在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
您最近一年使用:0次