The formula for the distance between two points in the plane is:
[tex]d=\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]So:
[tex]\begin{gathered} (x_1,y_1)=(5,5) \\ (x_2,y_2)=(-3,7) \\ d=\sqrt[]{(5-(-3))^2+(5-7)^2} \\ d=\sqrt[]{(8)^2+(-2)^2} \\ d=\sqrt[]{64+4} \\ d=\sqrt[]{68} \\ d=8.2462\ldots\approx8.2 \end{gathered}[/tex]So, the distance is approximately 8.2 units.
