Question

The Frostburg-Truth bus travels on a straight road from Frostburg Mall to Sojourner Truth Park. The mall is 3 miles west and 2 miles south of the City Center. The park is 4 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?

Answer 1

To start, write your locations as points, with north and south being positive and negative y respectively and east and west being positive and negative x respectively. Doing this gives us the mall at (-3,-2) and the park at (4,5). Now, we use our distance formula $( \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 } )$ to solve for the unknown distance. Plugging in with the park values as our second values and our mall values as our first values (as well as with our unknown distance as d), we get $d= \sqrt{(4-(-3))^2+(5-(-2))^2} = \sqrt{(7)^2+(7)^2} = \sqrt{49+49} = \sqrt{98}$. This square root can be rounded to 9.9 miles.