Elementary Geometry for College Students (5th Edition)

Published by Brooks Cole
ISBN 10: 1439047901
ISBN 13: 978-1-43904-790-3

Chapter 1 - Section 1.3 - Early Definitions and Postulates - Exercises: 16

Answer

X=8 AB=36

Work Step by Step

We know a midpoint divides a segment into 2 segments of equal length. Therefore, AM = MB, so we can set their equations equal to each other. 2(x+1)=3(x-2) 2x+2=3x-6 8=x So, x is 8. Next, the question asks us to solve for AB. Since AM=MB, and AM+MB=AB through the Segment Addition Postulate, 2AM=AB (Or 2 MB=AB, or AM+MB=AB) Substituting x into the equation for AM gives 2(8+1), or 18 Substituting x into the equation for MB gives 3(8-2), or 18 By addition OR multiplication, depending on how you solve it, AB=36
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