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新人教版高中英语选修2Unit 4 Journey Across a Vast Land教学设计
当孩子们由父母陪同时，他们才被允许进入这个运动场。3．过去分词(短语)作状语时的几种特殊情况(1)过去分词(短语)在句中作时间、条件、原因、让步状语时，相当于对应的时间、条件、原因及让步状语从句。Seen from the top of the mountain (＝When it is seen from the top of the mountain), the whole town looks more beautiful.从山顶上看，整个城市看起来更美了。Given ten more minutes (＝If we are given ten more minutes), we will finish the work perfectly.如果多给十分钟，我们会完美地完成这项工作。Greatly touched by his words (＝Because she was greatly touched by his words), she was full of tears.由于被他的话深深地感动，她满眼泪花。Warned of the storm (＝Though they were warned of the storm), the farmers were still working on the farm.尽管被警告了风暴的到来，但农民们仍在农场干活。(2)过去分词(短语)在句中作伴随、方式等状语时，可改为句子的并列谓语或改为并列分句。The teacher came into the room, followed by two students (＝and was followed by two students)．后面跟着两个学生，老师走进了房间。He spent the whole afternoon, accompanied by his mom(＝and was accompanied by his mom)．他由母亲陪着度过了一整个下午。
新人教版高中英语选修2Unit 1 Science and Scientists-Learning about Language教学设计
Step 7: complete the discourse according to the grammar rules.Cholera used to be one of the most 1.__________ (fear) diseases in the world. In the early 19th century, _2_________ an outbreak of cholera hit Europe, millions of people died. But neither its cause, 3__________ its cure was understood. A British doctor, John Snow, wanted to solve the problem and he knew that cholera would not be controlled _4_________ its cause was found. In general, there were two contradictory theories 5 __________ explained how cholera spread. The first suggested that bad air caused the disease. The second was that cholera was caused by an _6_________(infect) from germs in food or water. John Snow thought that the second theory was correct but he needed proof. So when another outbreak of cholera hit London in 1854, he began to investigate. Later, with all the evidence he _7_________ (gather), John Snow was able to announce that the pump water carried cholera germs. Therefore, he had the handle of the pump _8_________ (remove) so that it couldn't be used. Through his intervention，the disease was stopped in its tracks. What is more, John Snow found that some companies sold water from the River Thames that __9__________________ (pollute) by raw waste. The people who drank this water were much more likely _10_________ (get) cholera than those who drank pure or boiled water. Through John Snow's efforts, the _11_________ (threaten) of cholera around the world saw a substantial increase. Keys： 1.feared 2.when 3. nor 4.unless 5.that/which 6.infection 7.had gathered 8.removed 9.was polluted 10.to get 11. threat
新人教版高中英语选修2Unit 2 Bridging Cultures-Discovering useful structures教学设计
The grammar of this unit is designed to review noun clauses. Sentences that use nouns in a sentence are called noun clauses. Nominal clauses can act as subject, object, predicate, appositive and other components in compound sentences. According to the above-mentioned different grammatical functions, nominal clauses are divided into subject clause, object clause, predicate clause and appositive clause. In this unit, we will review the three kinds of nominal clauses. Appositive clauses are not required to be mastered in the optional compulsory stage, so they are not involved.1. Guide the students to judge the compound sentences and determine the composition of the clauses in the sentence.2. Instruct students to try to learn grammar by generalizing grammar rules, controlling written practice, and semi-open oral output.3. Inspire the students to systematize the function and usage of noun clause1.Instruct students to try to learn grammar by generalizing grammar rules, controlling written practice, and semi-open oral output.2.Inspire the students to systematize the function and usage of noun clauseStep1: The teacher ask studetns to find out more nominal clauses from the reading passage and udnerline the nominal clauses.
新人教版高中英语选修2Unit 5 First Aid-Discovering useful structures教学设计
You have no excuse for not going.你没有理由不去。He was punished for not having finished his homework.他因未完成作业而受到惩罚。2．动词ing形式复合结构由物主代词或人称代词宾格、名词所有格或普通格加动词ing，即“sb./sb.'s＋doing”构成。动词ing形式的复合结构实际上是给动词ing形式加了一个逻辑主语。动词ing形式的复合结构有四种形式：①形容词性物主代词＋动词ing②名词所有格＋动词ing③代词宾格＋动词ing④名词＋动词ingHer coming to help encouraged all of us.她来帮忙鼓舞了我们所有人。The baby was made awake by the door suddenly shutting.这个婴儿被突然的关门声吵醒了。Can you imagine him/Jack cooking at home?你能想象他/杰克在家做饭的样子吗？无生命名词无论是作主语还是作宾语都不能用第②种形式。Tom's winning first prize last year impressed me a lot.汤姆去年得了一等奖使我印象深刻。Do you mind my/me/Jack's/Jack leaving now?你介意我/杰克现在离开吗？Excuse me for my not coming on time．很抱歉我没能按时来。His father's being ill made him worried.他父亲病了，他很担心。We are looking forward to the singer's/the singer to give us a concert.我们盼望着这位歌手来给我们举办一场演唱会。
新人教版高中英语选修2Unit 1 Science and Scientists-Reading and thinking教学设计
Step 5： After learning the text, discuss with your peers about the following questions:1.John Snow believed Idea 2 was right. How did he finally prove it?2. Do you think John Snow would have solved this problem without the map?3. Cholera is a 19th century disease. What disease do you think is similar to cholera today?SARS and Covid-19 because they are both deadly and fatally infectious, have an unknown cause and need serious public health care to solve them urgently.keys:1. John Snow finally proved his idea because he found an outbreak that was clearly related to cholera, collected information and was able to tie cases outside the area to the polluted water.2. No. The map helped John Snow organize his ideas. He was able to identify those households that had had many deaths and check their water-drinking habits. He identified those houses that had had no deaths and surveyed their drinking habits. The evidence clearly pointed to the polluted water being the cause.3. SARS and Covid-19 because they are both deadly and fatally infectious, have an unknown cause and need serious public health care to solve them urgently.Step 6: Consolidate what you have learned by filling in the blanks:John Snow was a well-known _1___ in London in the _2__ century. He wanted to find the _3_____ of cholera in order to help people ___4_____ it. In 1854 when a cholera __5__ London, he began to gather information. He ___6__ on a map ___7___ all the dead people had lived and he found that many people who had ___8____ (drink) the dirty water from the __9____ died. So he decided that the polluted water ___10____ cholera. He suggested that the ___11__ of all water supplies should be _12______ and new methods of dealing with ____13___ water be found. Finally, “King Cholera” was __14_____.Keys: 1. doctor 2. 19th 3.cause 4.infected with 5.hit 6.marked 7.where 8.drunk 9.pump 10.carried 11.source 12.examined 13.polluted 14.defeatedHomework: Retell the text after class and preview its language points
新人教版高中英语选修2Unit 1 Science and Scientists-Using langauge教学设计
This happens because the dish soap molecules have a strong negative charge, and the milk molecules have a strong positive charge. Like magnets, these molecules are attracted to each other, and so they appear to move around on the plate, taking the food coloring with them, making it look like the colors are quickly moving to escape from the soap.Listening text:? Judy: Oh, I'm so sorry that you were ill and couldn't come with us on our field trip. How are you feeling now? Better?? Bill: Much better, thanks. But how was it?? Judy: Wonderful! I especially liked an area of the museum called Light Games.it was really cool. They had a hall of mirrors where I could see myself reflected thousands of times!? Bill: A hall of mirrors can be a lot of fun. What else did they have?? Judy: Well, they had an experiment where we looked at a blue screen for a while, and then suddenly we could see tiny bright lights moving around on it. You'll never guess what those bright lights were!? Bill: Come on, tell me!? Judy: They were our own blood cells. For some reason, our eyes play tricks on us when we look at a blue screen, and we can see our own blood cells moving around like little lights! But there was another thing I liked better. I stood in front of a white light, and it cast different shadows of me in every color of the rainbow!? Bill: Oh, I wish I had been there. Tell me more!? Judy: Well, they had another area for sound. They had a giant piano keyboard that you could use your feet to play. But then, instead of playing the sounds of a piano, it played the voices of classical singers! Then they had a giant dish, and when you spoke into it, it reflected the sound back and made it louder. You could use it to speak in a whisper to someone 17 meters away.? Bill: It all sounds so cool. I wish I could have gone with you? Judy: I know, but we can go together this weekend. I'd love to go there again!? Bill: That sounds like a great idea!
新人教版高中英语选修2Unit 3 Food and Culture-Discovering useful structures教学设计
The newspaper reported more than 100 people had been killed in the thunderstorm.报纸报道说有一百多人在暴风雨中丧生。(2)before、when、by the time、until、after、once等引导的时间状语从句的谓语是一般过去时，以及by、before后面接过去的时间时，主句动作发生在从句的动作或过去的时间之前且表示被动时，要用过去完成时的被动语态。By the time my brother was 10, he had been sent to Italy.我弟弟10岁前就已经被送到意大利了。Tons of rice had been produced by the end of last month. 到上月底已生产了好几吨大米。(3) It was the first/second/last ... time that ...句中that引导的定语从句中，主语与谓语构成被动关系时，要用过去完成时的被动语态。It was the first time that I had seen the night fact to face in one and a half years. 这是我一年半以来第一次亲眼目睹夜晚的景色。(4)在虚拟语气中，条件句表示与过去事实相反，且主语与谓语构成被动关系时，要用过去完成时的被动语态。If I had been instructed by him earlier, I would have finished the task.如果我早一点得到他的指示，我早就完成这项任务了。If I had hurried, I wouldn't have missed the train.如果我快点的话，我就不会误了火车。If you had been at the party, you would have met him. 如果你去了晚会，你就会见到他的。
新人教版高中英语选修2Unit 3 Food and Culture-Reading and thinking教学设计
The discourse explores the link between food and culture from a foreign’s perspective and it records some authentic Chinese food and illustrates the cultural meaning, gerography features and historic tradition that the food reflects. It is aimed to lead students to understand and think about the connection between food and culture. While teaching, the teacher should instruct students to find out the writing order and the writer’s experieces and feelings towards Chinese food and culture.1.Guide the students to read the text, sort out the information and dig out the topic.2.Understand the cultural connotation, regional characteristics and historical tradition of Chinese cuisine3.Understand and explore the relationship between food and people's personality4.Guide the students to use the cohesive words in the text5.Lead students to accurately grasp the real meaning of the information and improve the overall understanding ability by understanding the implied meaning behind the text.1. Enable the Ss to understand the structure and the writing style of the passage well.2. Lead the Ss to understand and think further about the connection between food and geography and local character traits.Step1: Prediction before reading. Before you read, look at the title, and the picture. What do you think this article is about?keys:It is about various culture and cuisine about a place or some countries.
小班数学教案 复习几何图形
【活动准备】 1、小兔手偶一个、魔术袋一个。 2、不同大小、不同颜色的圆形、三角形、正方形若干。 3、纸制小路（上面镂刻不同形状、不同大小、不同颜色的图形）。 【活动过程】 1、创设情境，引起幼儿参与活动的兴趣。 森林里，小兔的房子被大风吹倒了，我们一起帮它造一座房子吧。 2、帮小兔造房子，复习几何图形。 引导幼儿从魔术袋里摸出不同图形，并用摸出的几何图形给小兔造房子，复习圆形、三角形、正方形。
中班数学教案：认识几何图形
2、通过情景游戏等活动，让幼儿初步感知图形之间的转换关系，并能想办法解决问题。 3、培养幼儿思维的灵活性，发展幼儿动手能力，激发幼儿学习数学的欲望。活动准备： 1、学会了各种图形的特征。 2、自制的“小路”，上面镂刻大小不同的图形“土坑”，将镂刻下来的图形作成铺路的“石头”。小篮同幼儿人数。 3、圆形、三角形、长方形、正方形的图形标记，音乐。 活动过程： 一、情景导入“捡石头”，激发幼儿活动兴趣。 1、“小朋友，今天的天气真好，我们一起去郊外捡石头！”（随音乐进入活动室） 2、教师提出操作要求：“快看！有那么多五彩缤纷的小石头，大家可以挑自己喜欢的捡。”
领导在疫情防控领导指挥部组长会议上的讲话范文
一、要绷紧思想之弦，不可有丝毫麻痹大意 目前全球疫情仍在持续发展，国内新一轮疫情正在持续发酵，西安、安徽、江苏等多个省份出现聚集性疫情，新变异毒株也已登陆内地，加之随着旅游业复苏、高校学生返乡、人员流动比较多，防控压力陡然增加，这点我们在思想上要引起高度重视，清醒认识现阶段疫情防控形势的严峻性复杂性，针对新形势、新任务和新要求，提高政治站位，把做好当前疫情防控工作作为坚定捍卫“两个确立”、坚决做到“两个维护”的具体行动。坚决克服麻痹思想、厌战情绪、松劲心态，坚持实事求是，坚持我们防控工作中被实践证明行之有效的好办法，做到既不层层加码、也不放松警惕，切实筑牢疫情防线，进一步巩固来之不易的疫情防控成果。 刚刚会议对各专责组分工进行了再次明确，大家要以“时时放心不下”的责任感，担当作为、求真务实，进一步压紧压实疫情防控责任，保持思想不松、职责不变、力量不减，切实做好疫情防控工作。要全面激活指挥体系，各专责组要保持应急状态，强化联防联控、统筹协调，分工负责、密切配合，畅通信息、高效运转，做到统一领导、统一指挥、统一行动。紧跟疫情形势变化和工作要求，聚焦重点领域、关键环节，理性分析、科学研判，因时因势动态调整防控策略，第一时间落实管控措施，从严从实开展督导，形成工作闭环，坚决防止失管漏查和层层加码等现象；要加大抗疫先进典型的宣传力度，注重疫情防控工作和稳生产保供应中涌现的典型人物和事迹挖掘，激发广大干部员工干事创业的责任感使命感荣誉感，同时要做好疫情信息发布和舆论宣传，教育引导全员配合做好疫情防控相关工作。
书籍三国演义读后感参考范文
后来黄盖率领十艘大船，装满干柴和枯草，在上面浇了油，盖了麻布，驶向了北岸的乌林。在距离曹操的军营不远时，黄盖让各艘船的人点火，冲向了曹操的军营。当时的曹营被攻成成一片火海，曹操的士兵被烧的死的死，逃的逃。曹操只好带着亲信逃走了。 这场战役，败在了曹操轻信了黄盖的苦肉计，又因士兵是北方人，不识水性，在陆地上他们是精锐之师，但遇到了水，他们的就成了乌合之众了。加上曹操又太轻敌，总把自己想得太强大，才会掉以轻心，最终使这场战役失败。
《平凡的世界》阅读心得范文大全
在全县几千名考生中，他名列第三被录取了。他的学生生涯随着这张录取通知书的到来，也就完全终结了！”为了那个家牺牲的太多，他没日没夜的忙碌着，但是所有的努力都是为了那个家，似乎从来都没有为自己“自私”一下。这就是孙少安，孙家的长子。这个耿直，质朴的农村男子，他善良，能吃苦，有责任心，同时血气方刚，真心地爱着润叶。但是，却因为他身为农家，面对受过高等教育的润叶，爱，却没有勇气，爱，却自卑。他，最终错过了润叶。同样，因为局限的小农意识，他娶了x姑娘，生活便代替了爱情，与一个自己不曾爱过的人过起了柴米油盐的日子，他们相互扶持，紧紧依靠直到老去，一切平淡，生活便是真实的生活了。
4.23世界读书日国旗下讲话稿范文
大家早上好：冬天的远去，春天的伊始，迎来了这个充满书香的节日——世界读书日。阅读是一种兴趣，也是一种需要;阅读是一种积累，也是一种成长。相比之下，历史风云，战争演义类的作品《三国》，《水浒》会被男生津津乐道;而女生刚往往偏爱于描摹生活，抒发个人情感的作品如《简爱》，《红楼梦》等。我们徜徉在书的世界，遨游知识的海洋，我们以牛角挂书的李密，僧寺夜读的王冕，书编三绝的孔子，还有创造马背书馆、昆山无书趣读的顾炎武为榜样，乘着梦想的云梯青云直上。莎士比亚曾经说过：生活里没有书籍，好像没有阳光;智慧里没有书籍，就好像鸟儿没有翅膀。阅读对人成长的影响是巨大的，腹有诗书气自华，阅读一本好书往往能改变人的一生。我们读史书，看历史的残缺与完美，时局的动荡与平静，世界的无奈与精彩，生活的苦涩与醉人。每一段历史都是一支锈迹斑驳的利剑，在光华黯淡中，闪烁着一尊尊成败英雄的不灭精魂。
读书节主题国旗下讲话稿范文
亲爱的老师，同学们：大家上午好!在这秋天的晨曦中，有一种书香在这里飘逸，有一个主题这里激活，有一份快乐这里绽放。在这金桂飘香的季节里，我们裕安小学迎来了第一届读书节。 著名文学家冰心奶奶曾经说过：读书好，多读书，读好书。著名作家海伦凯勒也曾说过：一本好书像一艘船，带领着我们从狭隘的地方，驶向生活的无限海洋。是的，书是人类进步的阶梯，无论是严谨雄辩的哲学思想，还是奥妙无穷的科学知识，无论是精美绝伦的唐诗宋词，还是神奇有趣的神话传说，无不以书的形式传承至今。它记载着人类的文明。读书，既能丰富我们的知识，开拓我们的视野，又能陶冶我们的情操，还能让我们学会思考问题的方法、学到新的本领手捧书籍，就是手捧希望;开卷读书，就是打开世界之窗。开卷有益，一本好书就如明灯一样，能给人以指引。读一本好书，就是交一个品德高尚的有思想的朋友。 古今中外，大凡有所成就之人，都是热爱读书，与书为友的人，因为在书中，你可以和历史上最伟大的人物交谈，你可以和人类最优秀的思想对话;读书，还能让我们学到最优秀、最规范的语言。那些优秀的文学作品，字字句句都散发着珍珠般的光泽。在这个美好的季节，让我们把读书活动真正作为一次新的耕耘和播种，让迷人的浓浓书香飘溢在我们的校园，让读书成为我们实小人的习惯，让读书融入我们实小人的骨血，让读书伴随着我们快乐成长!最后祝愿大家在读书节里有丰硕的收获。 我的发言完毕，谢谢大家!
领导在市委指挥部调度工作会议上的讲话范文
一、要盯紧人员、货物摸排管控不放松 我市疫情防控的关键是“外防输入”，任务就是做好重点地区人员、货物的管控。刚才社区村居防控组对人员摸排管控工作进行了重点部署，各镇街要严格按照工作要求，切实抓好网格化摸排管控，织密织牢疫情防控摸排网。同时要高度重视货物防控工作，各工作组、行业部门和镇街要持续抓好“四个源头”管控，不断加强对境外来人、冷链物品、外来非冷链普通物品、从国内重点地区以及其他地区的来栖返栖人员的管控力度，严格进口冷链食品、非冷链物品预防性消毒和核酸检测，抓好邮政快递疫情防控措施落实，切实做到“人物同防、人物同查、人物同检”，精准有效防范疫情输入风险。这里特别强调几点：①关于既往感染者的规范管理工作。各镇街要从严做好解除居家健康监测不满*个月的既往感染者的摸排工作，务必不漏一人，核酸检测推进组负责做好单人单管核酸检测，及时关注反馈核酸检测结果。②关于居家健康监测人员管控工作。社区村居组牵头，各镇街具体负责，要严格落实“五包一”、上门核酸检测等措施，坚决不能出现因人员看管不到位导致疫情传播风险的问题。③关于进口货物管理。进口货物专班要严格抓好“冷链”“非冷链”两个线条的管理，从严做好报备审批、预防性消毒等措施，规范做好从业人员个人防护，同时要加强桌面推演和实景演练，不断提升应对复杂问题能力。 二、要严格做好社会面管控 从*月*日招远市解除封控到现在已经有近*个月的时间。这是今年以来，继*月份*区疫情、*月份*疫情后，我们经历的常态化时间最长的一次。随之而来是社会面警惕性的放松，特别是部分群众对戴口罩、测温、亮码、扫描场所码的防疫要求又开始懈怠了。大家必须清醒的认识到，疫情还远没有结束，防控一刻都不能放松。各行业主管部门要结合当前疫情防控形势，从严做好社会面管控工作，特别是暑期将至，我们即将迎来大学生返乡、中学生放假等人员返乡潮，社区村居防控组牵头要提前做好意愿返栖人员摸排工作，提前对接落实管控措施。文旅部门要深刻吸取北京天堂超市酒吧事件教训，从严做好KTV、影院等娱乐场所的管控。对于其他门头店、商场超市、农贸市场、农村大集、养老机构、学校、建筑工地等重点场所，各行业主管部门和镇街要切实担负起监管责任和属地责任，从严督促做好各项防控工作，真严、真管确保守牢守好全市疫情防控工作底线。
国旗下的讲话：踏上深阅读之旅
尊敬的各位老师，亲爱的同学们：大家上午好！我是高一、29班的王xx。夏日炎炎，心气浮躁，不如安静地坐下来，手捧一古卷，细细思量，最是书香能致远。今天我国旗下讲话的主题就是踏上深阅读之旅。阅读对人的成长影响是巨大的，一本好书往往能改变人的一生。生活中，因为读了一本书，而使人的命运有了根本性改变的比比皆是。读书不仅是一个人的修养标志之一，而且也应该成为人们完善自我、塑造自我、提升自我和凝聚智慧的重要途径之一。新教育的发起人——-朱永新教授说“一个人的精神发育史就是他的阅读史”“一个民族的精神境界很大程度上取决于这个民族的阅读水平”“一个没有阅读的学校也不可能有真正的教育”。而今在这个信息高度发展的竞速时代，随着网络的进一步发展，人们却忽视了阅读，快餐文化盛行。顾名思义，所谓快餐，只突现快，文化快餐既缺乏内涵，也不可能体现和代表主流，多啃也会无益，从而导致浅阅读泛滥。一目十行地浏览，只把视野停留在了书本的表面，把读书当作娱乐与消遣，读书也就失去了意义。这种形式化的阅读不如不读。更为严重的是，应该读书的人偏偏不读书。
大班诗歌《诗歌》说课稿
它将太阳在四季里变成了不同的颜色,在孩子们的幻想中,用生动而简洁的语言勾勒了一幅美丽的画面,绿色、金色、红色、彩色这些美丽的色彩都代表了每一季节的太阳,把孩子们带入一个快乐美好的幻想世界中。要想让幼儿理解和体会到诗歌中的内容,感受诗歌的美,就必须对诗歌中所提到的各种景色和事物有所了解,知道它们之间的依存关系。这是理解这首诗歌的知识基础也是本次活动的知识点。所以我准备在课前可以利用散步活动、谈话活动引导幼儿观察认识诗歌中所提到的这些事物,如感受太阳的温暖,观察了解太阳的颜色,四季中的变化及与我们人类的关系等,让幼儿亲身感受生活中大自然的美,为诗歌教学的开展奠定了情感基础。《纲要》中指出“要培养幼儿初步的发现美、感受美、表现美的情趣和能力。”的要求,及幼儿园语言教学的任务,制定了三个教学目标:1、在理解诗歌内容的基础上,感悟太阳的可爱、体会文中的意境,初步尝试有感情的朗诵诗歌。2、能大胆表达,发展口语表达能力,培养欣赏为学作品的兴趣和想象力,并进行仿编诗歌的尝试。
空间向量基本定理教学设计人教A版高中数学选择性必修第一册
反思感悟用基底表示空间向量的解题策略1.空间中,任一向量都可以用一个基底表示,且只要基底确定,则表示形式是唯一的.2.用基底表示空间向量时,一般要结合图形,运用向量加法、减法的平行四边形法则、三角形法则,以及数乘向量的运算法则,逐步向基向量过渡,直至全部用基向量表示.3.在空间几何体中选择基底时,通常选取公共起点最集中的向量或关系最明确的向量作为基底,例如,在正方体、长方体、平行六面体、四面体中,一般选用从同一顶点出发的三条棱所对应的向量作为基底.例2.在棱长为2的正方体ABCD-A1B1C1D1中,E,F分别是DD1,BD的中点,点G在棱CD上,且CG=1/3 CD(1)证明:EF⊥B1C;(2)求EF与C1G所成角的余弦值.思路分析选择一个空间基底,将(EF) ?,(B_1 C) ?,(C_1 G) ?用基向量表示.(1)证明(EF) ?·(B_1 C) ?=0即可;(2)求(EF) ?与(C_1 G) ?夹角的余弦值即可.(1)证明:设(DA) ?=i,(DC) ?=j,(DD_1 ) ?=k,则{i,j,k}构成空间的一个正交基底.
两点间的距离公式教学设计人教A版高中数学选择性必修第一册
一、情境导学在一条笔直的公路同侧有两个大型小区,现在计划在公路上某处建一个公交站点C,以方便居住在两个小区住户的出行.如何选址能使站点到两个小区的距离之和最小?二、探究新知问题1.在数轴上已知两点A、B，如何求A、B两点间的距离？提示：|AB|＝|xA－xB|.问题2：在平面直角坐标系中能否利用数轴上两点间的距离求出任意两点间距离？探究.当x1≠x2，y1≠y2时，|P1P2|＝？请简单说明理由．提示：可以，构造直角三角形利用勾股定理求解．答案：如图，在Rt △P1QP2中，|P1P2|2＝|P1Q|2＋|QP2|2，所以|P1P2|＝?x2－x1?2＋?y2－y1?2.即两点P1(x1，y1)，P2(x2，y2)间的距离|P1P2|＝?x2－x1?2＋?y2－y1?2.你还能用其它方法证明这个公式吗？2．两点间距离公式的理解(1)此公式与两点的先后顺序无关，也就是说公式也可写成|P1P2|＝?x2－x1?2＋?y2－y1?2.(2)当直线P1P2平行于x轴时，|P1P2|＝|x2－x1|.当直线P1P2平行于y轴时，|P1P2|＝|y2－y1|.
