# 1.3 Using Midpoint and Distance Formulas.pdf - 1.3 COMMON...

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Section 1.3Using Midpoint and Distance Formulas19Using Midpoint and Distance Formulas1.3!""#\$%&'( *+#"%&,\$!""#\$%&'( *+#"%&,\$How can you nd the midpoint and length of a line segment in a coordinate plane?Finding the Midpoint of a Line SegmentWork with a partner. Use centimeter graph paper.a.Graph AB, where the points and Bare as shown.b.Explain how to bisectAB that is, to divide ABinto two congruent line segments. Then bisect ABand use the result to nd the midpointMof AB HSG-CO.D.12Preparing for StandardHSG-GPE.B.7OREA, .c.What are the coordinates of the midpoint Md.Compare the x-coordinates of AB, and M. Compare the y-coordinates of A, B, and How are the coordinates of the midpoint Mrelated to the coordinates of Aand BFinding the Length of a Line SegmentWork with a partner. Use centimeter graph paper.a.Add point Cto your graph as shown.OF PROBLEMSTo be pro cient in math, you need to check your answers and continually ask yourself, “Does this make sense?”(-5, -2)24-2-4-2123456789101112131415? , M. ?b.Use the Pythagorean Theorem to nd the length of AB .c.Use a centimeter ruler to verify the length you found in part (b).d.Use the Pythagorean Theorem and point from Exploration 1to nd the lengths of and MB . What can you conclude?4-2-4244-22-44MAM
3.How can you nd the midpoint and length of a line segment in a coordinate plane?4.Find the coordinates of the midpoint Mand the length of the line segment whose endpoints are given.
MAKING SENSE OF PROBLEMSTo be pro cient in math, you need to check your answers and continually ask yourself, “Does this make sense?”(-5, -2)24-2-4-2123456789101112131415Learning StandardHSG-CO.D.12Preparing for StandardHSG-GPE.B.7ORE
B(-5, -2)24-2-4-2123456789101112131415
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ntimeter graph paper.123456789101112131415
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20Chapter 1Basics of Geometry1.3Lesson!"#\$ &'( !)** +,#-.!"#\$ &'( !)** +,#-.Find segment lengths using midpoints and segment bisectors.Use the Midpoint Formula.Use the Distance Formula.Midpoints and Segment BisectorsFinding Segment LengthsIn the skateboard design, VWbisects XYat point T, and XT=39.9 cm. Find XY.SOLUTIONPoint Tis the midpoint of XY . So, XT=TY=39.9 cm.XY=XT+TY Segment Addition Postulate(Postulate 1.2)=39.9+39.9 Substitute.=79.8 Add.So, the length of XY is 79.8 centimeters.Help in English and Spanish at BigIdeasMath.comIdentify the segment bisector of PQ . Then nd PQ.1. PMNQ1782. PMQ227midpoint,p. 20segment bisector,p. 20!"#\$ &"'()*+(#,!"#\$ &"'()*+(#,/'-,/'-,/'.0,1\$/'.0,1\$Midpoints and Segment BisectorsThe midpointof a segment is the point that divides the segment into two congruent segments. AMBMis the midpoint of AB . So, AM MB and AM =MB.A segment bisectoris a point, ray, line, line segment, or plane that intersects the segment at its midpoint. A midpoint or a segment bisector bisectsa segment.AMDCBCD is a segment bisector of AB . So, AM MB and AM =MB.READINGThe word bisectmeans “to cut into two equal parts.” XT=Ttee=39 9 cm39.9 cm.XVWYTIFP
Section 1.3Using Midpoint and Distance Formulas21Using Algebra with Segment LengthsPoint Mis the midpoint of VW. Find the length of VM.
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