2.(2010哈尔滨)如图,在平面直角坐标系中,点O是坐标原点,四边形AOCB是梯形,AB∥OC,点A的坐标为(0,8),点C的坐标为(10,0),OB=OC.
(1)求点B的坐标;
(2)点P从C点出发,沿线段CO以5个单位/秒的速度向终点O匀速运动,过点P作PH⊥OB,垂足为H,设△HBP的面积为S(S≠0),点P的运动时间为t秒,求S与t之间的函数关系式(直接写出自变量t的取值范围);
(3)在(2)的条件下,过点P作PM∥CB交线段AB于点M,过点M作MR⊥OC,垂足为R,线段MR分别交直线PH、OB于点E、G,点F为线段PM的中点,连接EF,当t为何值时,
?
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(2010台州市)
22.类比学习:一动点沿着数轴向右平移3个单位,再向左平移2个单位,相当于向右平移1个单位.用实数加法表示为 3+(
)=1.
若坐标平面上的点作如下平移:沿x轴方向平移的数量为a(向右为正,向左为负,平移
个单位),沿y轴方向平移的数量为b(向上为正,向下为负,平移
个单位),则把有序数对{a,b}叫做这一平移的“平移量”;“平移量”{a,b}与“平移量”{c,d}的加法运算法则为
.
解决问题:(1)计算:{3,1}+{1,2};{1,2}+{3,1}.
(2)①动点P从坐标原点O出发,先按照“平移量”{3,1}平移到A,再按照“平移量”
{1,2}平移到B;若先把动点P按照“平移量”{1,2}平移到C,再按照“平移量”
{3,1}平移,最后的位置还是点B吗? 在图1中画出四边形OABC.
②证明四边形OABC是平行四边形.
(3)如图2,一艘船从码头O出发,先航行到湖心岛码头P(2,3),再从码头P航行到码头Q(5,5),最后回到出发点O. 请用“平移量”加法算式表示它的航行过程.
解:(1){3,1}+{1,2}={4,3}. ……………………………………………2分
{1,2}+{3,1}={4,3}. …………………………………………………………………2分
(2)①画图 …………………………………………………2分
最后的位置仍是B.……………………………………1分
② 证明:由①知,A(3,1),B(4,3),C(1,2)
∴OC=AB=
=
,OA=BC=
=
,
∴四边形OABC是平行四边形.…………………………3分
(3){2,3}+{3,2}+{-5,-5}={0, 0}.……………………2分
1.(2010哈尔滨)如图,在△ABC中,∠ACB=90°,AC=BC=10,在△DCE中,
∠DCE=90°,DC=EC=6,点D在线段AC上,点E在线段BC
的延长线上.将△DCE绕点C旋转60°得到△D′CE′(点D的
对应点为点D′,点E的对应点为点 E′),连接AD′、BE′,
过点C作CN⊥ BE′,垂足为N,直线CN交线段AD′于点M,
则MN的长为 .
There are many types of reports. A report is simply an account of something 1 has happened. The commonest are news reports. We get them in newspapers, 2 the radio, and on television. The main purpose of a newspaper 3 (provide) news. If you examine a newspaper 4 (close), you will find that there are all types of news: accident, floods, fires, wars, fashions, sports, books, etc. The news 5 (cover) everything that happens to people and their surroundings. Sometimes there 6 (be) news items which are very amusing. A news report is usually very short, except 7 it is about something very important. It is also written in short paragraphs. The first paragraph is in fact 8 summary of the news item. The other paragraph give full details of the subject. There 9 (情态动词) also be interviews with people. Often there are photographs to 10 (动词短语) the news to make it more interesting. K^S*5U.C#O
10. He is said _____________(travel) around the country for 3 times.
9. A cook will be immediately fired if he is found ____________(smoke) in the kitchen.
8. So many people ______________(look) at her, she couldn’t speak out a single word.
7. His attention ______________(fix) his own research work, he did not even notice the loudly noise around him.
6. The criminal was about to tell the truth _______________ he was shot.
5.________________(accept) as a member of the company, he took over the job of the former secretary.
4. ________________(receive) her letter for a long time, I phoned her to see what was wrong.
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