首页
外语
计算机
考研
公务员
职业资格
财经
工程
司法
医学
专升本
自考
实用职业技能
登录
外语
P, Q, and R are three points in a plane, and R does not lie on line PQ. Which of the following is true about the set of all poin
P, Q, and R are three points in a plane, and R does not lie on line PQ. Which of the following is true about the set of all poin
admin
2014-08-13
59
问题
P, Q, and R are three points in a plane, and R does not lie on line PQ. Which of the following is true about the set of all points in the plane that are the same distance from all three points?
选项
A、It contains no points.
B、It contains one point.
C、It contains two points.
D、It is a line.
E、It is a circle.
答案
B
解析
First consider just two of the three points, say P and Q, and the set of points in the plane that are the same distance from them. Clearly the midpoint of line segment PQ is such a point. Are there others? You may recall from geometry that the points on the line that bisects PQ and is perpendicular to PQ are all the points that are equidistant from P and Q. Similarly, the points in the plane that lie on the perpendicular bisector of line segment PR are all the points that are equidistant from points P and R.
Because R does not lie on line PQ, line segments PQ and PR do not lie on the same line, and so their respective perpendicular bisectors are not parallel. Therefore, you can conclude that the two perpendicular bisectors intersect at a point. The point of intersection is on both perpendicular bisectors, so it is equidistant from P and Q as well as from P and R. Therefore, the point of intersection is equidistant from all three points. Are there any other points that are equidistant from P, Q, and R ? If there were, they would be on both perpendicular bisectors, but in fact only one point lies on both lines. The correct answer is Choice B.
转载请注明原文地址:https://kaotiyun.com/show/x5kO777K
本试题收录于:
GRE QUANTITATIVE题库GRE分类
0
GRE QUANTITATIVE
GRE
相关试题推荐
WhenIwasyoung,Ispentmysummervacationsonmygrandparents’farm.ThesummerthatIgraduatedfromcollege,I【C1】______my
Caraccidentskillmorethanonemillionpeopleandinjureapproximately50millioneachyear.【C1】______,millionsoffishcans
Caraccidentskillmorethanonemillionpeopleandinjureapproximately50millioneachyear.【C1】______,millionsoffishcans
AsTheplanecircledovertheairport,everyonesensedthatsomethingwaswrong.Theplanewasmovingunsteadilythroughtheair
Allthefollowingcasesareon-the-jobsmokingexceptthat______.Manymanagersdonotseemtobeinfavorofon-the-jobsmokin
Somepsychologists(心理学家)maintainthatmentalactssuchasthinkingarenotperformedinthebrainalone,butthatone’smuscl
NocountryintheworldhasmoredailynewspapersthantheUSA.Therearealmost2,000ofthem,ascomparedwith180inJapan,
Itwasacoldwinterday.AwomandroveuptotheRainbowBridgetollbooth(收费站)."I’mpayingformyself,andforthesixcarsb
Itwasacoldwinterday.AwomandroveuptotheRainbowBridgetollbooth(收费站)."I’mpayingformyself,andforthesixcarsb
IstheperimeteroftriangleABCgreaterthan20?(1)BC-AC=10(2)theareaoftangleABCis20.
随机试题
意见这一文种()
使慢性粒细胞白血病达到血液学缓解的首选药物是
感冒患者,恶寒发热轻微,但以脘腹冷痛,呕吐,腹泻为主要症状,舌苔薄,脉紧。其病机是
某测绘公司,持有乙级测绘资质,在一次测绘活动中擅自将持有的l:5万比例尺地形图进行复制,提交给外资公司使用,被该市国家安全部门查处。测绘资质审批机关应给予其()的处罚。
根据《建设工程质量管理条例》,工程监理单位转让工程监理业务的,责令改正,没收违法所得,处()的罚款。
根据以下资料,回答86-90题。据国家统计局2008年4月公布,2008年3月份,“国房景气指数”为104.72,比2月份回落0.83点,比去年同期上升3.50点。具体的各分类指数情况如下:3月份资金来源分类指数为102.38,比2月份
政策性金融机构是指那些由政府或政府机构发起、出资创立、参股或保证的,不以利润最大化为经营目的,在特定的业务领域内从事政策性融资活动,以贯彻和配合政府的社会经济政策或意图的金融机构。根据上述定义,下列选项不属于政策性金融机构的是()。
Refertotheexhibit.AfteraRIProuteismarkedinvalidonRouter_1,howmuchtimewillelapsebeforethatrouteisremovedfr
一个栈的初始状态为空。现将元素1,2,3,A,B,C依次入栈,然后再依次出栈,则元素出栈的顺序是
A、Theyhaveendlessenergy.B、Theyfeellowinspirits.C、Theybecomeangryeasily.D、Theycan’tcontroltheiremotions.A原文直现。
最新回复
(
0
)