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Distance and the Pythagorean Theorem Practice
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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)
units

Answer 1

To find the length between landmark B (Washington Monument) and landmark F (National Gallery of Art), we can use the Pythagorean theorem.

The coordinates of the points are as follows:
- Point B: (5, 9)
- Point F: (14, 8)

We can denote the coordinates as:
- \( x_1 = 5 \), \( y_1 = 9 \) (for point B)
- \( x_2 = 14 \), \( y_2 = 8 \) (for point F)

The formula for the distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by:

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

Substituting the coordinates:

\[
d = \sqrt{(14 - 5)^2 + (8 - 9)^2}
\]
\[
d = \sqrt{(9)^2 + (-1)^2}
\]
\[
d = \sqrt{81 + 1}
\]
\[
d = \sqrt{82}
\]
\[
d \approx 9.055
\]

Rounding this to the nearest hundredth, the length between landmark B and F is approximately:

**9.06 units.**