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 distance between landmark B and F, we can use the grid and scale provided.
Since the scale shows 200 feet and 200 meters, we can assume that each unit on the grid represents 200 feet or 200 meters.
Using the grid coordinates, we can find the horizontal and vertical distances between the two landmarks.
The horizontal distance between B and F is 14 units - 5 units = 9 units.
The vertical distance between B and F is 8 units - 9 units = -1 unit (since F is above B).
Now we can calculate the actual distance using the scale.
9 units * 200 feet/unit = 1800 feet (horizontal distance)
1 unit * 200 feet/unit = 200 feet (vertical distance)
Using the Pythagorean theorem, we can find the length between B and F.
Length = √((1800 feet)^2 + (200 feet)^2)
Length ≈ 1813.13 feet
Rounded to the nearest hundredth, the length between landmark B and F is approximately 1813.13 feet.
To find the length between landmark B and F, we need to calculate the distance between their respective grid points on the map.
First, let's find the coordinates for landmark B and F:
- Landmark B is located at 5 units across and 9 units down.
- Landmark F is located at 14 units across and 8 units down.
Now, we can calculate the distance between them using the distance formula, which is derived from the Pythagorean theorem:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Using the coordinates of B (5,9) and F (14,8), we can substitute them into the formula:
Distance = √((14 - 5)^2 + (8 - 9)^2)
Distance = √(9^2 + (-1)^2)
Distance = √(81 + 1)
Distance = √82
Distance ≈ 9.06 units
Since the map does not provide a scale for the units, we cannot determine the actual distance in feet or meters. We can only provide the distance in terms of grid units, which is approximately 9.06 units.
To find the length between landmark B (Washington Monument) and F (National Gallery of Art), we need to use the scale provided in the image. The scale shows that 17 units across on the grid represents 200 meters.
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 across.
Since 17 units on the grid represents 200 meters, we can set up a proportion to find the actual distance between B and F:
17 units = 200 meters
9 units = ?
Let's solve for the missing distance:
9 units * (200 meters / 17 units) = 105.882 meters
Therefore, the length between landmark B and F is approximately 105.882 meters. Rounded to the nearest hundredth, it is approximately 105.88 meters.
@BotGPT35, for clarification, points B and F are located 1 unit down and 9 units to the left, how do I solve that using the Pythagorean theorem
Apologies for the confusion. If points B and F are located 1 unit down and 9 units to the left, we can calculate the horizontal and vertical distances between them using the Pythagorean theorem.
The horizontal distance between B and F is 9 units.
The vertical distance between B and F is 1 unit.
To find the distance between B and F, we can apply the Pythagorean theorem:
Distance = √((horizontal distance)^2 + (vertical distance)^2)
Distance = √((9)^2 + (1)^2)
Distance = √(81 + 1)
Distance = √82
Distance ≈ 9.06 units
Therefore, the length between landmark B and F is approximately 9.06 units.