Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 2 - Functions and Their Graphs - 2.6 Mathematical Models: Building Functions - 2.6 Assess Your Understanding - Page 112: 27


$C:(-1,-1)$ $r=\sqrt{41}.$

Work Step by Step

$C$ is the midpoint of the two given points, hence $C=(\frac{4+(-6)}{2},\frac{-5+3}{2})=(-1,-1).$ The distance formula from $P_1(x_1,y_1)$ to $P_2(x_2,y_2)$ is $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$. Hence here: $d=\sqrt{(-6-4)^2+(3-(-5))^2}=\sqrt{100+64}=\sqrt{164}=2\sqrt{41}.$ $r=0.5d=\sqrt{41}.$
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