College Algebra: Concepts Through Functions, 4th Edition Test Bank

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Ch.0Foundations:APreludetoFunctions0.1TheDistanceandMidpointFormulas1UsetheDistanceFormulaMULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.Plotthepoint.1) (3,5)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6A)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6B)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6C)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6D)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6Page1

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2) (-6,5)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6A)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6B)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6C)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6D)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6Page2

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3) (3,-4)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6A)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6B)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6C)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6D)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6Page3

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4) (-3,-4)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6A)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6B)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6C)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6D)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6Page4

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5) (0,1)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6A)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6B)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6C)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6D)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6Page5

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6) (-4,0)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6A)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6B)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6C)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6D)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6Tellinwhichquadrantoronwhatcoordinateaxisthepointlies.7) (13,9)A) QuadrantIB) QuadrantIIC) QuadrantIIID) QuadrantIV8) (-10,20)A) QuadrantIIB) QuadrantIC) QuadrantIIID) QuadrantIV9) (-7,-12)A) QuadrantIIIB) QuadrantIC) QuadrantIID) QuadrantIV10) (16,-18)A) QuadrantIVB) QuadrantIC) QuadrantIID) QuadrantIIIPage6

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11) (0,-6)A) y-axisB) x-axisC) QuadrantID) QuadrantII12) (-2,0)A) x-axisB) y-axisC) QuadrantID) QuadrantIIFindthedistanced(P1,P2)betweenthepointsP1 andP2.13)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6A) 22B) 2C) 5D) 314)x-8-6-4-22468y8642-2-4-6-8x-8-6-4-22468y8642-2-4-6-8A)145B)17C) 72D) 1Page7

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15)x-8-6-4-22468y8642-2-4-6-8x-8-6-4-22468y8642-2-4-6-8A) 25B) 123C) 12D) 616)x-8-6-4-22468y8642-2-4-6-8x-8-6-4-22468y8642-2-4-6-8A) 229B) 8421C) 84D) 617) P1=(-2,-2);P2=(-2,4)A) 6B)6C) 7D) 518) P1=(4,-2);P2=(-1,10)A) 13B) 169C) 14D) 2619) P1=(0,7);P2=(-8,7)A) 8B) 7C)113D) 6420) P1=(0,0);P2=(-10,-2)A) 226B) 104C) 12D) 2321) P1=(1,5);P2=(-6,-6)A)170B) 62C) 77D) 422) P1=(7,-6);P2=(5,-2)A) 25B) 123C) 12D) 6Page8

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23) P1=(-3,-3);P2=(5,-7)A) 45B) 483C) 48D) 1224) P1=(-0.2,0.8);P2=(-2.4,-1.4)Roundtothreedecimalplaces,ifnecessary.A) 3.111B) 22C) 9.839D) 3.211Decidewhetherornotthepointsaretheverticesofarighttriangle.25) (-9,2),(0,2),(0,5)A) YesB) No26) (2,-4),(4,0),(6,-1)A) YesB) No27) (-10,-2),(-4,0),(-5,-5)A) NoB) Yes28) (8,-7),(14,-5),(20,-12)A) NoB) YesSolvetheproblem.29) Findallvaluesofksothatthegivenpointsare29unitsapart.(-5,5),(k,0)A)-3,-7B)-7C) 3,7D) 730) FindtheareaoftherighttriangleABCwithA=(-2,7),B=(7,-1),C=(3,9).A) 29squareunitsB) 58squareunitsC)582squareunitsD)292squareunits31) Findallthepointshavinganx-coordinateof9whosedistancefromthepoint(3,-2)is10.A) (9,6),(9,-10)B) (9,2),(9,-4)C) (9,-12),(9,8)D) (9,13),(9,-7)32) Amiddleschoolʹsbaseballplayingfieldisasquare,60 feetonaside.Howfarisitdirectlyfromhomeplatetosecondbase(thediagonalofthesquare)?Ifnecessary,roundtothenearestfoot.A) 85feetB) 86feetC) 84 feetD) 92feet33) Amotorcycleandacarleaveanintersectionatthesametime.Themotorcycleheadsnorthatanaveragespeedof20milesperhour,whilethecarheadseastatanaveragespeedof48milesperhour.Findanexpressionfortheirdistanceapartinmilesattheendofthours.A) 52tmilesB) t68milesC) 52tmilesD) 2t13milesPage9

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34) FindthelengthofeachsideofthetriangledeterminedbythethreepointsP1,P2,andP3.Statewhetherthetriangleisanisoscelestriangle,arighttriangle,neitherofthese,orboth.P1=(-5,-4),P2=(-3,4),P3=(0,-1)A) d(P1,P2)=217;d(P2,P3)=34;d(P1,P3)=34bothB) d(P1,P2)=217;d(P2,P3)=34;d(P1,P3)=34isoscelestriangleC) d(P1,P2)=217;d(P2,P3)=34;d(P1,P3)=52righttriangleD) d(P1,P2)=217;d(P2,P3)=34;d(P1,P3)=52neither2UsetheMidpointFormulaMULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.FindthemidpointofthelinesegmentjoiningthepointsP1 andP2.1) P1=(2,6);P2=(8,3)A) (5,92 )B) (10,9)C) (-6,3)D) ( 92 ,5)2) P1=(-7,9);P2=(4,1)A)-32 ,5B)-112 ,4C)-11,8D)-3,103) P1=(7,1);P2=(-16,-16)A)-92 ,-152B)232 ,172C)-9,-15D) 9,154) P1=(-0.8,0.7);P2=(-2.7,2.2)A) (-1.75,1.45)B) (1.45,-1.75)C) (-0.95,0.75)D) (0.75,-0.95)5) P1=(a,4);P2=(0,7)A)a2 ,112B) a,11C)-a2 ,3D) a,1126) P1=(5x,8);P2=(6x,9)A)11x2,172B) 11x,17C) x,1D)17x2,112Solvetheproblem.7) If(2,2)istheendpointofalinesegment,and(7,5)isitsmidpoint,findtheotherendpoint.A) (12,8)B) (12,-1)C) (-8,-4)D) (8,12)8) If(3,-5)istheendpointofalinesegment,and(2,-10)isitsmidpoint,findtheotherendpoint.A) (1,-15)B) (1,0)C) (5,5)D) (-7,-7)9) If(-8,-6)istheendpointofalinesegment,and(-5,-11)isitsmidpoint,findtheotherendpoint.A) (-2,-16)B) (-2,-1)C) (-14,4)D) (-18,0)Page10

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10) If(-7,5)istheendpointofalinesegment,and(-10,6)isitsmidpoint,findtheotherendpoint.A) (-13,7)B) (-13,4)C) (-1,3)D) (-5,-1)11) Themediansofatriangleintersectatapoint.Thedistancefromthevertextothepointisexactlytwo-thirdsofthedistancefromthevertextothemidpointoftheoppositeside.FindtheexactdistanceofthatpointfromthevertexA(3,4)ofatriangle,giventhattheothertwoverticesareat(0,0)and(8,0).A) 2173B)173C) 2D) 830.2GraphsofEquationsinTwoVariables;Intercepts;Symmetry1GraphEquationsbyPlottingPointsMULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.Determinewhetherthegivenpointisonthegraphoftheequation.1) Equation:y=x4-xPoint:(-9,6558)A) NoB) Yes2) Equation:x2-y2=4Point:(2,2)A) NoB) YesPage11

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Graphtheequationbyplottingpoints.3) y=x+6x-10-5510y105-5-10x-10-5510y105-5-10A)x-10-5510y105-5-10x-10-5510y105-5-10B)x-10-5510y105-5-10x-10-5510y105-5-10C)x-10-5510y105-5-10x-10-5510y105-5-10D)x-10-5510y105-5-10x-10-5510y105-5-10Page12

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4) y=2x-6x-10-5510y105-5-10x-10-5510y105-5-10A)x-10-5510y105-5-10x-10-5510y105-5-10B)x-10-5510y105-5-10x-10-5510y105-5-10C)x-10-5510y105-5-10x-10-5510y105-5-10D)x-10-5510y105-5-10x-10-5510y105-5-10Page13

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5) y=x2-9x-10-5510y105-5-10x-10-5510y105-5-10A)x-10-5510y105-5-10x-10-5510y105-5-10B)x-10-5510y105-5-10x-10-5510y105-5-10C)x-10-5510y105-5-10x-10-5510y105-5-10D)x-10-5510y105-5-10x-10-5510y105-5-10Page14

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6) 4x+2y=8x-10-5510y105-5-10x-10-5510y105-5-10A)x-10-5510y105-5-10x-10-5510y105-5-10B)x-10-5510y105-5-10x-10-5510y105-5-10C)x-10-5510y105-5-10x-10-5510y105-5-10D)x-10-5510y105-5-10x-10-5510y105-5-10Page15

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