Question

1. the frosdburg dush bus travels on a straight road from frosdburg mall to sejourner truth park. the mall is 5 miles west and 3 miles south of the city center. the park is 4 miles east and 4 miles north of the center. how far is it from the mall to the park to the nearest tenth of a mile?

○ 1.4 miles

○ 5.8 miles

○ 5.7 miles

○ 11.4 miles

Explanation:

Step1: Define coordinates

Let City Center be at \((0,0)\). Mall: 5 miles west (\(x = -5\)) and 3 miles south (\(y = -3\)) → \((-5, -3)\). Park: 4 miles east (\(x = 4\)) and 4 miles north (\(y = 4\)) → \((4, 4)\).

Step2: Apply distance formula

Distance \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)
Substitute \((x_1,y_1)=(-5,-3)\), \((x_2,y_2)=(4,4)\):
\(d = \sqrt{(4 - (-5))^2 + (4 - (-3))^2}\)
\(d = \sqrt{(9)^2 + (7)^2}\)
\(d = \sqrt{81 + 49}\)
\(d = \sqrt{130} \approx 11.4\)? Wait, no—wait, the options have 11.4? Wait, no, maybe I misread. Wait, the question: "how far is it from the mall to the park as the raven flies (straight line)?" Wait, the options: 1.4, 5.8, 5.7, 11.4. Wait, recalculate:

Wait, \(x\)-difference: \(4 - (-5) = 9\), \(y\)-difference: \(4 - (-3) = 7\). Then \(d = \sqrt{9^2 + 7^2} = \sqrt{81 + 49} = \sqrt{130} \approx 11.4\). So the answer is 11.4 miles.

Answer:

11.4 miles (corresponding to the option with "11.4 miles")