The Frostburg-Truth bus travels on a straight road from Frostburg Mall to Sojourner Truth Park. The mall is 3 miles west and 4 miles south of the City Center. The park is 3 miles east and 5 miles north of the Center. How far is it from the mall to the park to the nearest tenth of a mile?
5.8 miles
5.0 miles
1.0 mile
10.8 miles
To determine the distance from the mall to the park, we can break down the problem into the horizontal and vertical components. The horizontal distance is 3 miles west from the mall to the City Center, and then 3 miles east from the Center to the park, resulting in a total horizontal distance of 3 + 3 = 6 miles.
The vertical distance is 4 miles south from the mall to the City Center, and then 5 miles north from the Center to the park, resulting in a total vertical distance of 4 + 5 = 9 miles.
Using the Pythagorean theorem, we can find the distance from the mall to the park:
Distance = √((horizontal distance)^2 + (vertical distance)^2)
= √(6^2 + 9^2)
= √(36 + 81)
= √117
≈ 10.8 miles
Therefore, the distance from the mall to the park is approximately 10.8 miles, which is closest to the last option: 10.8 miles.