Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 7 - Section 7.3 - Simplifying Radicals, the Distance Formula, and Circles - 7.3 Exercises: 122


$2\sqrt{10} \text{ units}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the Distance Formula to find the distance between the given points $\left( -1,5 \right)$ and $\left( -7,7 \right)$. $\bf{\text{Solution Details:}}$ With the given points, then $x_1= -1 ,$ $x_2= -7 ,$ $y_1= 5 ,$ and $y_2= 7 .$ Using the Distance Formula which is given by $d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2} ,$ then \begin{array}{l}\require{cancel} d=\sqrt{(-1-(-7))^2+(5-7)^2} \\\\ d=\sqrt{(-1+7)^2+(5-7)^2} \\\\ d=\sqrt{(6)^2+(-2)^2} \\\\ d=\sqrt{36+4} \\\\ d=\sqrt{40} \\\\ d=\sqrt{4\cdot10} \\\\ d=\sqrt{(2)^2\cdot10} \\\\ d=2\sqrt{10} .\end{array} Hence, the distance is $ 2\sqrt{10} \text{ units} .$
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