Question

Your travel guide contains a grid map of New York, with each unit on the grid representing 0.125 miles is the Empire State building is located at (4,-4) in Central Park is located at (-14,8), which is the direct distance( Not walking distance, which would have to account for bridges in roadways) between the two landmarks in miles? Round your answer to two decimal places if necessary

Answer 1

Use the distance formula to solve for the direct distance from (4,-4) up to (-14,8)

$\begin{gathered} d = \sqrt {(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2} \\ d = \sqrt {(-14 - 4)^2 + (8 - (-4))^2} \\ d = \sqrt {(-18)^2 + (12)^2} \\ d = \sqrt {{324} + {144}} \\ d = \sqrt {468} \\ d=\sqrt{36\cdot13} \\ d=6\sqrt{13} \end{gathered}$

Since 1 grid is equal to 0.125 miles. Multiply the distance in units and we get

$6\sqrt{13}\cdot0.125\text{ miles}=2.704163457$

Rounding to 2 decimal places, the direct distance is 2.70 miles.