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)

1 answer

To find the length between landmark B (Washington Monument) and F (National Gallery of Art) on the map, we first need to determine their coordinates based on the grid provided:

  • Point B (Washington Monument) is located at (5, 9).
  • Point F (National Gallery of Art) is located at (14, 8).

Next, we can calculate the distance between these two points using the distance formula:

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Substituting the coordinates of point B (5, 9) and point F (14, 8) into the formula:

\[ d = \sqrt{(14 - 5)^2 + (8 - 9)^2} \]

Calculating the differences:

\[ d = \sqrt{(9)^2 + (-1)^2} \]

Now squaring the values:

\[ d = \sqrt{81 + 1} = \sqrt{82} \]

Next, we calculate \(\sqrt{82}\):

\[ d \approx 9.055 \]

To convert this distance to real-world units (assuming the scale provided is consistent for feet or meters), since we've determined the grid dimensions but haven't specified the units used, we'll provide the distance in the same units as the scale maximum (200 feet or 200 meters).

Since the grid size isn't specified, let's proceed to round it to the nearest hundredth:

Thus, the final rounded answer is:

\[ \text{Distance} \approx 9.06 \text{ units (in grid size)} \]

Please clarify the conversion to feet or meters if required, but the answer based on the grid units is approximately 9.06 units.