Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter F - Foundations: A Prelude to Functions - Section F.1 The Distance and Midpoint Formulas - F.1 Assess Your Understanding - Page 7: 19

Answer

$d=\sqrt{68}=2\sqrt{17}$

Work Step by Step

To calculate the distance $d$ between two points, we have: $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ Plug the $x$ and $y$ coordinates of the given points to obtain: $d=\sqrt{(5-3)^2+(4-(-4))^2}=\sqrt {4+64}=\sqrt{68}$ If we further simplify, then $d=\sqrt{68}=\sqrt{4(17)} = 2\sqrt{17}$
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