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
To find the distance between landmark B and F, we can use the Pythagorean theorem. Since the grid units on the map correspond to a scale of 200 feet and 200 meters, we can convert the grid units to feet.
The x-coordinate of B is 5 units and the x-coordinate of F is 14 units. So the horizontal distance between B and F is 14 - 5 = 9 units.
The y-coordinate of B is 9 units and the y-coordinate of F is 8 units. So the vertical distance between B and F is 9 - 8 = 1 unit.
Using the Pythagorean theorem, we can calculate the distance between B and F:
Distance^2 = horizontal distance^2 + vertical distance^2
Distance^2 = 9^2 + 1^2
Distance^2 = 81 + 1
Distance^2 = 82
Taking the square root of both sides, we get:
Distance = √82
Rounding to the nearest hundredth, the length between landmark B and F is approximately 9.06 units.
Distance and the Pythagorean Theorem Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
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Question
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)
units