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Find the length between landmark B and F . Round the answer to the nearest hundredth, if necessary. (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.
To find the distance between landmark B and F, we can use the distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Where x1 and y1 are the coordinates of landmark B (5, 9) and x2 and y2 are the coordinates of landmark F (14, 8).
Plugging in the values:
Distance = √((14 - 5)^2 + (8 - 9)^2)
= √(9^2 + (-1)^2)
= √(81 + 1)
= √82
Rounding to the nearest hundredth:
Distance ≈ 9.06
Therefore, the length between landmark B and F is approximately 9.06.
A graph shows quadrant 1 with the x-axis and y-axis ranging from 0 to positive 5. Data points marked are point A at left parenthesis 1 comma 2 right parenthesis, point B at left parenthesis 3 comma 2 right parenthesis, point C at left parenthesis 3 comma 4 right parenthesis, and point D at left parenthesis 1 comma 4 right parenthesis. A line joins points A to B, B to C, C to D, and D to A, forming a rectangle.
Apply the Pythagorean Theorem to find the length of the diagonal of the square. Round your answer to the nearest hundredth, if necessary.
(1 point)
Responses
4.24
8
4
2.83
To find the length of the diagonal of the square formed by the points, we can use the Pythagorean Theorem.
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the sides of the square are equal in length, so we can find the length of one side and then use the Pythagorean Theorem to find the length of the diagonal.
The length of one side of the square can be found using the distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
The distance between point A (1, 2) and point B (3, 2) is:
Distance AB = √((3 - 1)^2 + (2 - 2)^2)
= √(2^2 + 0^2)
= √(4 + 0)
= √4
= 2
The length of the diagonal of the square is the hypotenuse of a right triangle with legs of length 2.
By the Pythagorean Theorem, the length of the diagonal is:
Diagonal = √(2^2 + 2^2)
= √(4 + 4)
= √8
Rounding to the nearest hundredth:
Diagonal ≈ 2.83
Therefore, the length of the diagonal of the square is approximately 2.83.
A graph shows four quadrants with the x-axis and y-axis both ranging from negative 5 to positive 5 in increments of 1. Unlabeled data points marked are at left parenthesis negative 2 comma negative 1 right parenthesis, and at left parenthesis 2 comma 4 right parenthesis. A straight line joins the two lines with a positive slope.
Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth, if necessary.
(1 point)
Responses
6:40
41
5.57
9
To find the length between the two points, we can use the Pythagorean Theorem.
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the two points (-2, -1) and (2, 4) form the two sides of a right triangle, and we can use the distance formula to find the lengths of these sides.
The distance between the two points can be calculated as:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Using the given points:
Distance = √((2 - (-2))^2 + (4 - (-1))^2)
= √((4^2) + (5^2))
= √(16 + 25)
= √41
Rounding to the nearest hundredth:
Distance ≈ 6.40
Therefore, the length between the two points is approximately 6.40.
To find the length between landmark B and F, we need to calculate the distance between their respective coordinates on the grid.
Given:
- Point B is located at (5, 9).
- Point F is located at (14, 8).
We can use the distance formula to find the length between two points in a coordinate plane. The formula is:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Where (x1, y1) are the coordinates of the first point, and (x2, y2) are the coordinates of the second point.
Plugging in the values:
- x1 = 5
- y1 = 9
- x2 = 14
- y2 = 8
Distance = √((14 - 5)^2 + (8 - 9)^2)
= √(9^2 + (-1)^2)
= √(81 + 1)
= √82
≈ 9.06
Therefore, the length between landmark B and F is approximately 9.06 units.