Question

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)
a
units

Answer 1

To find the length between landmarks B (Washington Monument) and F (National Gallery of Art), we will use the distance formula.

The coordinates for points B and F are:
- B: (5, 9)
- F: (14, 8)

Using the distance formula:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
where \((x_1, y_1)\) are the coordinates of point B and \((x_2, y_2)\) are the coordinates of point F.

Substituting in the coordinates:
\[
d = \sqrt{(14 - 5)^2 + (8 - 9)^2}
\]
\[
d = \sqrt{(9)^2 + (-1)^2}
\]
\[
d = \sqrt{81 + 1}
\]
\[
d = \sqrt{82}
\]
\[
d \approx 9.06
\]

Therefore, the length between landmark B and landmark F is approximately **9.06 units**.