Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 7 - Section 7.3 - Simplifying Radical Expressions - Exercise Set: 95

Answer

$(\sqrt 2, \frac{\sqrt 5}{2})$

Work Step by Step

We know that the midpoint of the line segment whose endpoints are $(x_{1},y_{1})$ and $(x_{2},y_{2})$ is the point with coordinates $(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$. Therefore, a line with endpoints $(\sqrt 2,3\sqrt 5)$ and $(\sqrt 2,-2\sqrt 5)$ will have a midpoint of $(\frac{\sqrt 2+\sqrt 2}{2}, \frac{3\sqrt 5+(-2\sqrt 5)}{2})=(\frac{2\sqrt 2}{2}, \frac{\sqrt 5}{2})=(\sqrt 2, \frac{\sqrt 5}{2})$.
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