Use the image to answer the question.
A map shows a grid 17 units across and 12 units high, superimposed over shapes that represent streets and buildings. A key lists buildings located in Washington D.C. that correspond to points on the grid. Point A represents the White House. It is located at 4 units across from the left, and 3 units down from the top. Point B represents the Washington Monument, located at 5 units across and 9 units down. Point C represents the Natural History Museum, and is located at approximately 8 units across and 8 units down. Point D represents the Smithsonian, and is located at 10 units across and 10 units down. Point E represents the National Portrait Gallery, and is located at 12 units across and 3 units down. Point F represents the National Gallery of Art, and is located at 14 units across and 8 units down. A scale shows 200 feet and 200 meters.
Find the length between landmark B and F . Round the answer to the nearest hundredth, if necessary.
To find the length between landmark B (Washington Monument) and F (National Gallery of Art), we can use the grid points provided.
The x-coordinate of B is 5 units across and the x-coordinate of F is 14 units across. Therefore, the horizontal distance between B and F is 14 - 5 = 9 units.
The y-coordinate of B is 9 units down and the y-coordinate of F is 8 units down. Therefore, the vertical distance between B and F is 9 - 8 = 1 unit.
Using the scale provided, we can determine the distance in feet. Each unit on the grid represents 200 feet.
Therefore, the horizontal distance in feet is 9 units * 200 feet/unit = 1800 feet.
Since the vertical distance is only 1 unit, the distance in feet will still be 200 feet.
Using the Pythagorean theorem, we can find the length between B and F.
Length = √(horizontal distance^2 + vertical distance^2)
Length = √(1800^2 + 200^2)
Length = √(3240000 + 40000)
Length = √3280000
Length ≈ 1809.31 feet (rounded to the nearest hundredth)
Therefore, the length between landmark B and F is approximately 1809.31 feet.