【答案】
分析:(1)直線y=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155032504488808/SYS201310221550325044888023_DA/0.png)
x-6中,令y=0,x=0,可得A、B兩點(diǎn)坐標(biāo),過C點(diǎn)作CD⊥x軸,垂足為D,由△ACD∽△ABO,可求AD,CD,確定C點(diǎn)坐標(biāo);
(2)過D作X軸的垂線,交AB于Q,過F作Y軸的垂線FG,垂足是G,兩線交于N,得到則∠BQN=∠QFN=∠OBA,根據(jù)sin∠OBA=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155032504488808/SYS201310221550325044888023_DA/1.png)
,cos∠OBA=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155032504488808/SYS201310221550325044888023_DA/2.png)
,即可求出F的坐標(biāo);
(3)當(dāng)四邊形OBFE為梯形時(shí),且BF∥OE時(shí),根據(jù)則△ABO∽△BFC,得出
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155032504488808/SYS201310221550325044888023_DA/3.png)
=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155032504488808/SYS201310221550325044888023_DA/4.png)
,代入即可求出t=±8;同法可求:當(dāng)四邊形OBFE為梯形時(shí),且BO∥EF時(shí),t=12;當(dāng)四邊形BCFE為梯形時(shí),且BE∥CF時(shí),t=-4.5;當(dāng)四邊形BCFE為梯形時(shí),且BC∥EF時(shí),t=-12.
解答:解:(1)y=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155032504488808/SYS201310221550325044888023_DA/5.png)
x-6中,令y=0,x=0,可得A、B兩點(diǎn)坐標(biāo),
令y=0,得到0=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155032504488808/SYS201310221550325044888023_DA/6.png)
x-6,解得:x=8,∴A(8,0),
令x=0,解得:y=-6,∴B(0,-6),
在△AOB中由勾股定理得:AB=10,
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155032504488808/SYS201310221550325044888023_DA/images7.png)
∴AC=10-6=4,
過C點(diǎn)作CD⊥x軸,垂足為D,則△ACD∽△ABO,
∴
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155032504488808/SYS201310221550325044888023_DA/7.png)
=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155032504488808/SYS201310221550325044888023_DA/8.png)
=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155032504488808/SYS201310221550325044888023_DA/9.png)
,
∴
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155032504488808/SYS201310221550325044888023_DA/10.png)
=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155032504488808/SYS201310221550325044888023_DA/11.png)
=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155032504488808/SYS201310221550325044888023_DA/12.png)
,
∴AD=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155032504488808/SYS201310221550325044888023_DA/13.png)
,CD=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155032504488808/SYS201310221550325044888023_DA/14.png)
,
∴OD=8-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155032504488808/SYS201310221550325044888023_DA/15.png)
=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155032504488808/SYS201310221550325044888023_DA/16.png)
,
∴C(
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155032504488808/SYS201310221550325044888023_DA/17.png)
,-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155032504488808/SYS201310221550325044888023_DA/18.png)
);
答:A、B、C三點(diǎn)的坐標(biāo)分別是(8,0),(0,-6),(
![](http://img.manfen5.com/res/czsx/web/STSource/20131022155032504488808/SYS201310221550325044888023_DA/19.png)
,-
![](http://img.manfen5.com/res/czsx/web/STSource/20131022155032504488808/SYS201310221550325044888023_DA/20.png)
).
(2)過D作x軸的垂線,交AB于C,過F作y軸的垂線FG,垂足是G,兩線交于N,
過C作y軸的垂線CQ,垂足為Q,交y軸于點(diǎn)Q,
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155032504488808/SYS201310221550325044888023_DA/images22.png)
∵∠BCF=90°,∠CNF=90°,
∴∠BCN+∠NCF=90°,∠NCF+∠CFN=90°,
∴∠BCN=∠CFN,
又∠OBA+∠QCB=90°,∠BCN+∠QCB=90°,
∴∠BCN=∠OBA,
則∠BCN=∠CFN=∠OBA,
又OA=8,OB=6,
∵sin∠OBA=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155032504488808/SYS201310221550325044888023_DA/21.png)
,cos∠OBA=
![](http://img.manfen5.com/res/czsx/web/STSource/20131022155032504488808/SYS201310221550325044888023_DA/22.png)
,
∴sin∠CFB=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155032504488808/SYS201310221550325044888023_DA/23.png)
,cos∠CFB=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155032504488808/SYS201310221550325044888023_DA/24.png)
,
∵CF=OE=t,
∴GQ=CN=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155032504488808/SYS201310221550325044888023_DA/25.png)
t,F(xiàn)N=
![](http://img.manfen5.com/res/czsx/web/STSource/20131022155032504488808/SYS201310221550325044888023_DA/26.png)
t,
∵C(
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155032504488808/SYS201310221550325044888023_DA/27.png)
,-
![](http://img.manfen5.com/res/czsx/web/STSource/20131022155032504488808/SYS201310221550325044888023_DA/28.png)
),
∴F(
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155032504488808/SYS201310221550325044888023_DA/29.png)
+
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155032504488808/SYS201310221550325044888023_DA/30.png)
t,-
![](http://img.manfen5.com/res/czsx/web/STSource/20131022155032504488808/SYS201310221550325044888023_DA/31.png)
-
![](http://img.manfen5.com/res/czsx/web/STSource/20131022155032504488808/SYS201310221550325044888023_DA/32.png)
t),
答:點(diǎn)F的坐標(biāo)是F(
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155032504488808/SYS201310221550325044888023_DA/33.png)
+
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155032504488808/SYS201310221550325044888023_DA/34.png)
t,-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155032504488808/SYS201310221550325044888023_DA/35.png)
-
![](http://img.manfen5.com/res/czsx/web/STSource/20131022155032504488808/SYS201310221550325044888023_DA/36.png)
t).
(3)解:當(dāng)四邊形OBFE為梯形時(shí),且BF∥OE時(shí),則△ABO∽△BFC,
∴
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155032504488808/SYS201310221550325044888023_DA/37.png)
=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155032504488808/SYS201310221550325044888023_DA/38.png)
,
即
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155032504488808/SYS201310221550325044888023_DA/39.png)
=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155032504488808/SYS201310221550325044888023_DA/40.png)
,
解得:t=±
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155032504488808/SYS201310221550325044888023_DA/41.png)
;
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155032504488808/SYS201310221550325044888023_DA/images44.png)
同法可求:當(dāng)四邊形OBFE為梯形時(shí),且BO∥EF時(shí),
t=12;
![](http://img.manfen5.com/res/czsx/web/STSource/20131022155032504488808/SYS201310221550325044888023_DA/images45.png)
當(dāng)四邊形BCFE為梯形時(shí),且BE∥CF時(shí),t=-4.5;
![](http://img.manfen5.com/res/czsx/web/STSource/20131022155032504488808/SYS201310221550325044888023_DA/images46.png)
當(dāng)四邊形BCFE為梯形時(shí),且BC∥EF時(shí),t=-12,
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155032504488808/SYS201310221550325044888023_DA/images47.png)
答:在點(diǎn)E的運(yùn)動(dòng)過程中,存在著四邊形BCFE或OBFE為梯形,t的值是±
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155032504488808/SYS201310221550325044888023_DA/42.png)
或12或-12.
點(diǎn)評(píng):此題主要考查了一次函數(shù)的圖象上點(diǎn)的坐標(biāo)特征,相似三角形的性質(zhì)和判定,勾股定理,梯形,旋轉(zhuǎn)的性質(zhì)等知識(shí)點(diǎn),熟練地應(yīng)用這些性質(zhì)進(jìn)行計(jì)算是解決問題的關(guān)鍵.此題是一個(gè)拔高的題目,有一定的難度.