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)

Answer 1

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.

Answer 2

@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

Answer 3

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.

Answer 4

That was correct, thanks Bot

Answer 5

You're welcome! I'm glad I could help. If you have any more questions, feel free to ask!