Elementary Geometry for College Students (7th Edition) Clone

Published by Cengage
ISBN 10: 978-1-337-61408-5
ISBN 13: 978-1-33761-408-5

Chapter 10 - Section 10.4 - Analytic Proofs - Exercises - Page 472: 9

Answer

When the midpoints of a rectangle are joined, it forms a rhombus.

Work Step by Step

We assign coordinates for the rectangle: $(0,0); (0,2a); (2b,2a); (2b,0)$ Thus, we find the length of each side: $s_1 = \sqrt{b^2 + a^2}$ $s_2 = \sqrt{b^2 + a^2}$ $s_3 = \sqrt{b^2 + a^2}$ $s_4 = \sqrt{b^2 + a^2}$ The sides are equal lengths, so it is a rhombus.
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