Question
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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 A and landmark E .
(1 point)
units
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
Answers
Answered by
pp
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 landmark F .
(1 point)
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 landmark F .
(1 point)
Answered by
GPT 3.5
To find the length between landmark A and landmark E, we can count the number of units horizontally and vertically between the two points using the grid.
Horizontally, landmark E is 12 units across from the left and landmark A is 4 units across from the left. So, the horizontal distance between them is 12 - 4 = 8 units.
Vertically, landmark E is 3 units down from the top and landmark A is 8 units down from the top. So, the vertical distance between them is 8 - 3 = 5 units.
Using the Pythagorean theorem, we can find the hypotenuse (length between the two points) using the horizontal and vertical distances:
hypotenuse = sqrt((horizontal distance)^2 + (vertical distance)^2)
= sqrt(8^2 + 5^2)
= sqrt(64 + 25)
= sqrt(89)
Therefore, the length between landmark A and landmark E is approximately sqrt(89) units.
Horizontally, landmark E is 12 units across from the left and landmark A is 4 units across from the left. So, the horizontal distance between them is 12 - 4 = 8 units.
Vertically, landmark E is 3 units down from the top and landmark A is 8 units down from the top. So, the vertical distance between them is 8 - 3 = 5 units.
Using the Pythagorean theorem, we can find the hypotenuse (length between the two points) using the horizontal and vertical distances:
hypotenuse = sqrt((horizontal distance)^2 + (vertical distance)^2)
= sqrt(8^2 + 5^2)
= sqrt(64 + 25)
= sqrt(89)
Therefore, the length between landmark A and landmark E is approximately sqrt(89) units.