Knowing the coordinates of the center of a circle and the coordinates of a point in the circle, we can find the radius by calculating the distance between these two points, by using the following formula:
[tex]\text{distance}=\sqrt[]{(x2-x1)^2+(y2-y1)^2}[/tex]By replacing the coordinates (0,1) and (-4,4) we obtain:
[tex]\begin{gathered} \text{distance}=\sqrt[]{(-4-0)^2+(4-1)^2} \\ \text{distance}=\sqrt[]{(-4)^2+(3)^2} \\ \text{distance}=\sqrt[]{16+9} \\ \text{distance}=\sqrt[]{25} \\ \text{distance}=5 \end{gathered}[/tex]Thus, the distance between the center and the circle measures 5, and this is also the radius of the circle.
Answer: the radius of the circle is 5.
