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

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

$C$ 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: $d=\sqrt{(-6-4)^2+(3-(-5))^2}=\sqrt{100+64}=\sqrt{164}=2\sqrt{41}.$ $r=0.5d=\sqrt{41}.$