Question

PLEASE HELP!

The Frostburg-Truth bus travels from Frostburg Mall through the city's center to Sojourner Truth Park. The mall is 2 miles east and 2 miles north of the city's center. Truth Park is 3 miles west and 4 miles south of the city's center. How far is it from Truth Park to the mall, to the nearest tenth of a mile?
a.) 2.8
b.) 7.8
c.) 5
d.)2.2

Answer 1

It’s definitely not A or D I’d try B

Answer 2

Option: b is the correct answer.

b) 7.8 miles.

Explanation:

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:

`CM=√((2-0)^2+(2-0)^2)\\\\CM=√(4+4)\\\\CM=√(8)=2√(2)`

Hence,
`CM=2.828\ miles`

Similarly,

`PC=√((0-(-3))^2+(0-(-4))^2)\\\\\\PC=√(3^2+4^2)\\\\\\PC=√(9+16)\\\\\\PC=√(25)\\\\\\PC=5\ miles`

Hence, PM=2.828+5=7.828 miles

The distance between mall and Truth park to the nearest tenth is:

7.8 miles