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.
(1 point)
To find the length between landmark B and F, we need to find the horizontal and vertical distances between the two points.
Horizontal distance = 14 units - 5 units = 9 units
Vertical distance = 8 units - 9 units = -1 unit
Since the vertical distance is negative, we can ignore the negative sign and consider it as a distance of 1 unit.
Using the scale provided, we know that 17 units on the map represent 200 meters. Therefore, 1 unit represents 200 meters / 17 units = 11.76 meters.
To find the length between landmark B and F, we use the Pythagorean theorem:
Length = √(horizontal distance^2 + vertical distance^2)
= √(9 units^2 + 1 unit^2)
Using a calculator or rounding to the nearest hundredth:
Length = √(81 units^2 + 1 unit^2)
= √82 units
≈ 9.06 units
Since each unit represents 11.76 meters, we can multiply the length by the conversion factor:
9.06 units * 11.76 meters/unit ≈ 106.47 meters
Therefore, the length between landmark B and F is approximately 106.47 meters (rounded to the nearest hundredth).