Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10:
ISBN 13:

Chapter 10 - Section 10.4 - Analytic Proofs - Exercises - Page 464: 11

Answer

The midpoint of the hypotenuse of a right triangle is always an equal distance away from each of the vertices.

Work Step by Step

We call the vertices: $(0,0); (0,2b); (0,2a)$ Since the midpoint is on one side, we find that it is already known to be $d= \sqrt{b^2 +a^2} $ away from each vertex touching the hypotenuse. We use the distance formula from the origin to find: $d_2 =\sqrt{a^2+b^2}$ The two distances are equal.
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