Module3Lesson18DistanceontheCoordinatePlane.notebook March03,2014 Homework Review Lesson 17 1

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Module3Lesson18DistanceontheCoordinatePlane.notebook March03,2014 MODULE3RaonalNumbers TopicC:RaonalNumbers&theCoordinatePlane Lesson18:DistanceontheCoordinatePlane StudentOutcomes Studentscomputethelengthofhorizontalandvercallinesegmentswithintegercoordinatesforendpointsin thecoordinateplanebycounngthenumberofunitsbetweenendpointsandusingabsolutevalue. 3

Module3Lesson18DistanceontheCoordinatePlane.notebook March03,2014 OpeningExercise Fourfriendsaretouringonmotorcycles.Theycometoanintersectionoftwo roadstheroadtheyareoncontinuesstraight,andtheotherisperpendicularto it.Thesignattheintersectionshowsthedistancestoseveraltowns.Drawa map/diagramoftheroadsanduseitandtheinformationonthesigntoanswer thefollowingquestions: WhatisthedistancebetweenAlbertsvilleandDeweyFalls? WhatisthedistancebetweenBlossvilleandCheyenne? Onthecoordinateplane,whatrepresentstheintersectionofthetworoads? 4

Module3Lesson18DistanceontheCoordinatePlane.notebook March03,2014 Example1:TheDistanceBetweenPointsonanAxis Whatisthedistancebetween(4,0)and(5,0)? Whatdotheorderedpairshaveincommonandwhatdoesthatmeanabouttheirlocaoninthe coordinateplane? Bothoftheirycoordinatesarezerosoeachpointliesonthexaxis,thehorizontalnumber line. Howdidwendthedistancebetweentwonumbersonthenumberline? Wecalculatedtheabsolutevaluesofthenumbers,whichtoldushowfarthenumberswere fromzero.Ifthenumberswerelocatedonoppositesidesofzero,thenweaddedtheir absolutevaluestogether.Ifthenumberswerelocatedonthesamesideofzero,thenwe subtractedtheirabsolutevalues. Usethesamemethodtondthedistancebetween(4,0)and(5,0) 5

Module3Lesson18DistanceontheCoordinatePlane.notebook March03,2014 Example2:TheLengthofaLineSegmentonanAxis Whatisthelengthofthelinesegmentwithendpoints(0,6)and(0,11)? Whatdotheorderedpairsoftheendpointshaveincommonandwhatdoesthat meanaboutthelinesegmentslocaoninthecoordinateplane? Thexcoordinatesofbothendpointsarezerosothepointslieontheyaxis, thevercalnumberline.Ifitsendpointslieonavercalnumberline,then thelinesegmentitselfmustalsolieonthevercalline. Findthelengthofthelinesegmentdescribedbyndingthedistancebetweenits endpoints(0,6)and(0,11) 1identifytheline 2identifythedistances 3identifythelocations 4calculate 6

Module3Lesson18DistanceontheCoordinatePlane.notebook March03,2014 Example3:LengthofaHorizontalorVercalLineSegmentthat doesNotLieonanAxis Findthelengthofthelinesegmentwithendpoints(3,3)and(3,5) Whatdotheendpoints,whicharerepresentedbytheorderedpairs, haveincommon?Whatdoesthattellusaboutthelocaonofthe linesegmentonthecoordinateplane? Bothendpointshavexcoordinatesof3sothepointslie onthevercallinethatintersectsthexaxisat3.This meansthattheendpointsofthelinesegment,andthus thelinesegment,lieonavercalline. Findthelengthofthelinesegmentbyndingthedistancebetween itsendpoints. 1identifytheline 2identifythedistances 3identifythelocations 4calculate 7

Module3Lesson18DistanceontheCoordinatePlane.notebook March03,2014 1identifytheline 2identifythedistances 3identifythelocations Exercises 4calculate 1. Findthelengthsofthelinesegmentswhoseendpointsaregivenbelow.Explain howyoudeterminedthatthelinesegmentsarehorizontalorvercal. a. (3,4)and(3,9) b. (2,2)and(8,2) 8

Module3Lesson18DistanceontheCoordinatePlane.notebook March03,2014 c. (6,6)and(6,1) d. (9,4)and(4,4) e. (0,11)and(0,8) 1identifytheline 2identifythedistances 3identifythelocations 4calculate 9

Module3Lesson18DistanceontheCoordinatePlane.notebook March03,2014 Closing Whycanwendthelengthofahorizontalorvercallinesegmentevenifitsnotonthexoryaxis? Canyouthinkofarealworldsituaonwherethismightbeuseful? Please take out your exit ticket for Lesson 18, close your binder, and complete the exit ticket. This will be collected. 10

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