In general, the distance between two points on the plane is given by the formula below
[tex]d((x_1,y_1),(x_2,y_2))=\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]
Therefore, in our case,
[tex]\begin{gathered} \text{slide}=(-2,0) \\ \text{fountain}=(-2,-2) \\ \text{ Swings}=(5,2) \end{gathered}[/tex]
Thus,
[tex]\begin{gathered} d(slide,fountain)=\sqrt[]{(-2-(-2))^2+(0-(-2))^2}=\sqrt[]{0+2^2}=2 \\ \text{and} \\ d(swings,fountain)=\sqrt[]{(5-(-2))^2+(2-(-2))^2}=\sqrt[]{7^2}=7 \end{gathered}[/tex]
The answer to part a) is 2*100ft=200ft
The answer to part b) is 7*100ft=700ft
