Distance and the Pythagorean Theorem Practice
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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)
units
Using the Pythagorean Theorem, we can calculate the distance between points B and F:
First, we calculate the horizontal distance:
Horizontal distance = 14 - 5 = 9 units
Next, we calculate the vertical distance:
Vertical distance = 8 - 9 = -1 units
Now, we can use the Pythagorean Theorem to find the distance between B and F:
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.