Option: b is the correct answer.
b) 7.8 miles.
Let us suppose that the city center is located at C(0,0) on the coordinate grid.
Now, The mall is 2 miles east and 2 miles north of the city's center.
This means that the coordinate of the mall is located at M(2,2)
and Truth Park is 3 miles west and 4 miles south of the city's center.
This means that the coordinate of the Truth park is located at P(-3,-4)
Hence, the distance between the mall and Truth park is equal to the sum of the distance between the Center city and mall and center city and Truth park.
i.e. PM=CM+PC
From the figure we may observe that:
[tex]CM=\sqrt{(2-0)^2+(2-0)^2}\\\\CM=\sqrt{4+4}\\\\CM=\sqrt{8}=2\sqrt{2}[/tex]
Hence, [tex]CM=2.828\ miles[/tex]
Similarly,
[tex]PC=\sqrt{(0-(-3))^2+(0-(-4))^2}\\\\\\PC=\sqrt{3^2+4^2}\\\\\\PC=\sqrt{9+16}\\\\\\PC=\sqrt{25}\\\\\\PC=5\ miles[/tex]
Hence, PM=2.828+5=7.828 miles
The distance between mall and Truth park to the nearest tenth is:
7.8 miles
