Answer
Joining midpoints seems to construct the polygon's center.
Work Step by Step
I used intuition and a diagram, as per the problem's dictate.
Elementary Geometry for College Students (5th Edition)
by Alexander, Daniel C.; Koeberlein, Geralyn M.
Published by
Brooks Cole
ISBN 10:
1439047901
ISBN 13:
978-1-43904-790-3
Chapter 2 - Section 2.5 - Convex Polygons - Exercises - Page 106: 35
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