Question

Your travel guide contains a grid map of Washington D.C., with each unit on the grid representing 0.125 miles. If the Jefferson Memorial is located at (4,−2) and the Lincoln Memorial is located at (−4,5), what is the direct distance (not walking distance, which would have to account for bridges and roadways) between the two memorials in miles? Round your answer to two decimal places, if necessary.

Answer 1

Treating grid units as miles, the direct distance between the memorials is roughly 3.76 miles, calculated using the Pythagorean theorem on their coordinate differences.

To find the direct distance between the memorials, we can treat the grid like a coordinate plane.

- The horizontal distance is the difference in their x-coordinates: |-4 - (4)| = 8 units.

- The vertical distance is the difference in their y-coordinates: |5 - (-2)| = 7 units.

Now, using the Pythagorean theorem, we can find the total distance:

√(8 units^2 + 7 units^2) = √(113 units^2) = √(14.125 miles^2) ≈ 3.76 miles (rounded to two decimal places).

Therefore, the direct distance between the Jefferson Memorial and the Lincoln Memorial is approximately 3.76 miles.