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)
To find the length between landmark B and F, we need to calculate the distance between their coordinates on the grid.
Let's start by finding the horizontal distance between B and F.
The x-coordinate of B is 5 units across, and the x-coordinate of F is 14 units across.
Therefore, the horizontal distance between B and F is 14 - 5 = 9 units.
Next, we need to find the vertical distance between B and F.
The y-coordinate of B is 9 units down, and the y-coordinate of F is 8 units down.
Therefore, the vertical distance between B and F is 9 - 8 = 1 unit.
Using the given scale, we know that 17 units on the grid represents 200 meters.
Therefore, 1 unit on the grid represents 200/17 = 11.76 meters (rounded to the nearest hundredth).
Finally, we can calculate the distance between B and F using the Pythagorean theorem:
distance = √((horizontal distance)^2 + (vertical distance)^2)
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.
To find the length between landmark B and F, we need to use the scale provided. The scale shows that 17 units on the grid represent 200 feet and 200 meters.
First, let's find the horizontal distance between B and F. B is located at 5 units across and F is located at 14 units across. The difference between their horizontal positions is 14 - 5 = 9 units.
Since 17 units represent 200 feet, we can set up the proportion:
17 units / 9 units = 200 feet / x
Cross-multiplying, we get:
17x = 9 * 200
17x = 1800
Dividing both sides by 17, we find:
x = 1800 / 17 ≈ 105.88
So, the horizontal distance between B and F is approximately 105.88 feet.
Next, let's find the vertical distance between B and F. B is located at 9 units down and F is located at 8 units down. The difference between their vertical positions is 9 - 8 = 1 unit.
Since 12 units represent 200 meters, we can set up the proportion:
12 units / 1 unit = 200 meters / y
Cross-multiplying, we get:
12y = 1 * 200
12y = 200
Dividing both sides by 12, we find:
y = 200 / 12 ≈ 16.67
So, the vertical distance between B and F is approximately 16.67 meters.
Finally, to find the length between B and F, we can use the Pythagorean theorem since the distance is in a diagonal direction:
Length² = (vertical distance)² + (horizontal distance)²
Length² = 16.67² + 105.88²
Length² ≈ 277.56 + 11189.85
Length² ≈ 11467.41
Taking the square root of both sides, we find:
Length ≈ √11467.41 ≈ 107.06
Rounded to the nearest hundredth, the length between landmark B and F is approximately 107.06 units.
To find the length between landmark B and F, we need to calculate the distance between their respective grid points and then convert it to the actual length using the scale provided.
First, let's determine the distance between B and F on the grid.
The horizontal distance between B and F is given by the difference in their x-coordinates (across units). B is at 5 units across, and F is at 14 units across. So the horizontal distance is 14 - 5 = 9 units.
The vertical distance between B and F is given by the difference in their y-coordinates (down units). B is at 9 units down, and F is at 8 units down. So the vertical distance is 9 - 8 = 1 unit.
Now, let's convert this distance to actual length using the scale.
The scale provided is 200 feet and 200 meters, but since we're only interested in finding the distance between B and F in feet, we'll use the 200 feet scale.
We know that 17 units on the grid represent 200 feet.
So, to find the length between B and F, we can set up the following proportion:
9 units (grid distance) / 17 units (grid length) = x feet (actual length) / 200 feet (scale length)
Simplifying the proportion:
9/17 = x/200
Cross-multiplying:
9 * 200 = 17 * x
1800 = 17x
Dividing both sides by 17:
1800 / 17 ≈ 105.88
Rounding to the nearest hundredth:
The length between landmark B and F is approximately 105.88 feet.
Use the image to answer the question.A graph shows four quadrants with the x-axis and y-axis both ranging from negative 10 to positive 10 in increments of 1. Unlabeled points are plotted at left parenthesis negative 6 comma 8 right parenthesis, left parenthesis 4 comma 8 right parenthesis, left parenthesis 4 comma negative 3 right parenthesis, and left parenthesis negative 6 comma negative 3 right parenthesis. A straight line joins the four points forming a rectangle. What is the length of the diagonal of the rectangle? Round your answer to the nearest hundredth, if necessary.(1 point)
To find the length of the diagonal of the rectangle, we can use the distance formula.
The given points form a rectangle, with the points represented as:
Point 1: (-6, 8)
Point 2: (4, 8)
Point 3: (4, -3)
Point 4: (-6, -3)
We can find the length of each of the sides of the rectangle and then use the Pythagorean theorem to find the length of the diagonal.
Side 1:
The length of side 1 is the horizontal distance between point 1 and point 2.
Side 1 = |4 - (-6)| = 10
Side 2:
The length of side 2 is the vertical distance between point 2 and point 3.
Side 2 = |8 - (-3)| = 11
Side 3:
The length of side 3 is the horizontal distance between point 3 and point 4.
Side 3 = |(-6) - 4| = 10
Side 4:
The length of side 4 is the vertical distance between point 4 and point 1.
Side 4 = |8 - (-3)| = 11
Now, we can find the length of the diagonal using the Pythagorean theorem:
Diagonal² = Side 1² + Side 3²
Diagonal² = 10² + 10²
Diagonal² = 200
Taking the square root of both sides:
Diagonal ≈ √200 ≈ 14.14
Rounded to the nearest hundredth, the length of the diagonal of the rectangle is approximately 14.14.