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 A and landmark E .
(1 point)
units
To find the length between landmark A and landmark E, we can use the distance formula, which is derived from the Pythagorean Theorem.
The distance formula is:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Where (x1, y1) are the coordinates of landmark A and (x2, y2) are the coordinates of landmark E.
From the information given, we can determine that the coordinates for landmark A are (4, 3) and the coordinates for landmark E are (12, 3).
Plugging these values into the distance formula, we get:
d = √((12 - 4)^2 + (3 - 3)^2)
Simplifying further, we have:
d = √(8^2 + 0^2)
d = √(64 + 0)
d = √64
d = 8
Therefore, the length between landmark A and landmark E is 8 units.