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 landmark F . Round the answer to the nearest hundredth, if necessary.
(1 point)
To find the distance between landmark B and landmark F, we need to use the grid units and the scale provided in the map.
From the grid, we can see that landmark B is at 5 units across and 9 units down, and landmark F is at 14 units across and 8 units down.
To find the length between B and F, we need to calculate the horizontal and vertical distances separately.
Horizontal distance = 14 units - 5 units = 9 units
Vertical distance = 8 units - 9 units = -1 unit
Since the vertical distance is negative, it means we need to subtract the vertical distance instead of adding it.
Using the scale provided (200 feet and 200 meters), we can convert the grid units into feet or meters.
Assuming we convert it to feet, we have:
1 unit on the grid = 200 feet
So, the horizontal distance in feet = 9 units * 200 feet = 1800 feet
The vertical distance in feet = -1 unit * 200 feet = -200 feet
Now, we can use the Pythagorean theorem to find the length between B and F in feet:
Length^2 = horizontal distance^2 + vertical distance^2
Length^2 = 1800 feet^2 + (-200 feet)^2
Length^2 = 3240000 square feet + 40000 square feet
Length^2 = 3280000 square feet
Length ≈ √3280000 feet ≈ 1809.67 feet
Rounded to the nearest hundredth, the length between landmark B and landmark F is approximately 1809.67 feet.