# 1.3 Geometry Book -2.pdf - 1.3 TEKS G.5.A G.7.C G.8.C...

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Chapter 6 / Exercise 27
Elementary and Intermediate Algebra
Tussy/Gustafson
Expert Verified
1.3Use Midpoint and Distance Formulas15Use Midpoint andDistance Formulas1.3BeforeYou found lengths of segments.NowYou will find lengths of segments in the coordinate plane.Why?So you can find an unknown length, as in Example 1.Key Vocabularymidpointsegment bisectorSTEP 1 Draw}ABon a piece ofpaper.STEP 2 Foldthe paper so thatBis on top ofA.STEP 3 LabelpointM. CompareAM,MB, andAB.ACTIVITYFOLD ASEGMENTBISECTORMIDPOINTS AND BISECTORSThemidpointof a segment is the point thatdivides the segment into two congruent segments. Asegment bisectorisa point, ray, line, line segment, or plane th at intersects the segment at itsmidpoint. A midpoint or a segment bisectorbisectsa segment.Mis the midpoint of}AB.]CDis a segment bisector of}AB.So,}AM>}MBandAM5MB. So,}AM>}MBandAM5MB.EX AMPLE1Find segment lengthsSKATEBOARDIn the skateboard design,}VWbisects}XYatpointT, andXT539.9 cm. FindXY.SolutionPointTis the midpoint of}XY. So,XT5TY539.9 cm.XY5XT1TYSegment Addition Postulate539.9139.9Substitute.579.8 cmAdd.ABMABCDM48679G.5.A, G.7.C,G.8.CTEKS
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Chapter 6 / Exercise 27
Elementary and Intermediate Algebra
Tussy/Gustafson
Expert Verified
16Chapter 1Essentials of GeometryEX AMPLE2Use algebra with segment lengthsALGEBRAPointMis the midpointof}VW. Find the length of}VM.4x213x13SolutionSTEP 1 Writeand solve an equation. Use the fact that thatVM5MW.VM5MWWrite equation.4x2153x13Substitute.x2153Subtract 3xfrom each side.x54Add 1 to each side.STEP 2 Evaluatethe expression forVMwhenx54.VM54x2154(4)21515cSo, the length of}VMis 15.CHECK BecauseVM5MW, the length of}MWshould be 15. If you evaluatethe expression forMW, you should find thatMW515.MW53x1353(4)13515GUIDEDPRACTICEfor Examples 1 and 2In Exercises 1 and 2, identify the segment bisector of}PQ. Then findPQ.1.2.5x271122xMlPPCOORDINATE PLANEYou can use the coordinates of the endpoints of asegment to find the coordinates of the midpoint.READ DIRECTIONSAlways read directionlines carefully. Noticethat this direction linehas two parts.KEY CONCEPTFor Your NotebookThe Midpoint FormulaThe coordinates of the midpoint of asegment are the averages of thex-coordinates and of they-coordinatesof the endpoints.IfA(x1,y1) andB(x2,y2) are points in acoordinate plane, then the midpointMof}ABhas coordinates1x11x2}2,y11y2}22.xyx11x22x11x22y11y22y11y22x1x2y2y1MS,DMS,Dx11x22x11x22y11y22y11y22A(x1,y1)B(x2,y2)PMNP178VMWREVIEW ALGEBRAFor help with solvingequations, see p. 875.
1.3Use Midpoint and Distance Formulas17EX AMPLE3