题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017090222-65948.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017090223-23979.jpg)
(1)、求出b和k;
(2)、求证:△ACD是等腰直角三角形;
(3)、在y轴上是否存在点P,使
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017090223-39234.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017090223-66059.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017090223-66059.png)
解析
试题分析:(1)将已知点的坐标代入到两个函数的解析式即可求得k和b的值;
(2))根据直线x=-4与一次函数y=-x+3交于点D,求得点D(-4,7),根据直线x=-4与反比例函数y=-
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017090224-76056.png)
(3)过点A作AP1∥BC,交y轴于P1,则S△PBC=S△ABC,根据B(4,-1),C(-4,1)确定直线BC的解析式为y=-
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017090224-37191.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017090224-37191.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017090223-66059.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017090223-66059.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017090223-66059.png)
试题解析:(1)解:∵一次函数y=-x+b的图象经过点A(-1,4)
∴-(-1)+b=4,
即b=3,
又∵反比例函数
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017090222-65948.png)
∴k=xy=(-1)×4=-4;
(2)证明:∵直线l⊥x轴于点E(-4,0)则直线l解析式为x=-4,
∴直线x=-4与一次函数y=-x+3交于点D,则D(-4,7)
直线x=-4与反比例函数y=-
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017090224-76056.png)
则C(-4,1)
过点A作AF⊥直线l于点F,
∵A(-1,4),C(-4,1),D(-4,7)
∴CD=6,AF=3,DF=3,FC=3
又∵∠AFD=∠AFC=90°,
由勾股定理得:AC=AD=3
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017090224-62777.png)
又∵AD2+AC2=(3
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017090224-62777.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017090224-62777.png)
CD2=62=36
∴AD2+AC2=CD2
∴由勾股定理逆定理得:△ACD是直角三角形,
又∵AD=AC
∴△ACD是等腰直角三角形;
(3)解:过点A作AP1∥BC,交y轴于P1,则S△PBC=S△ABC
∵B(4,-1),C(-4,1)
∴直线BC的解析式为y=-
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017090224-37191.png)
∵设直线AP1的解析式为y=-
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017090224-37191.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017090223-66059.png)
∴P1(0,
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017090223-66059.png)
∴作P1关于x轴的对称点P2,则S△P1BC=S△P2BCBC=S△ABC,
故P2(0,-
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017090223-66059.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017090223-66059.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017090223-66059.png)
考点: 反比例函数综合题
核心考点
试题【如图,一次函数y=-x+b与反比例函数的图象相交于A(-1,4)、B(4,-1)两点,直线l⊥x轴于点E(-4,0),与反比例函数和一次函数的图象分别相交于点C】;主要考察你对反比例函数定义等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017090214-85022.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017090214-23655.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017090215-81797.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017090209-39615.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017090209-66695.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017090210-23118.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017090159-84148.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017090159-23170.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017090159-62392.png)
A.第一象限 | B.第二象限 | C.第三象限 | D.第四象限 |
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017090150-49377.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017090150-24004.png)
A.0 | B.0或1 | C.0或2 | D.4 |
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017090143-86421.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017090144-56031.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017090144-21194.png)
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A.![]() | B.![]() |
C.![]() | D.![]() |
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