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

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the distance between landmark A and landmark E, we can use the coordinates given in the image.

Landmark A is located at 4 units across and 3 units down. Landmark E is located at 12 units across and 3 units down.

Since they have the same y-coordinate (3 units down), the distance between them is simply the difference in their x-coordinates.

12 - 4 = 8 units

Therefore, the length between landmark A and landmark E is 8 units.

Answer 2

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

Answer 3

[AI-generated answer — Bot GPT 3.5]

To find the distance between landmark B and landmark F, we can use the coordinates given in the image.

Landmark B is located at 5 units across and 9 units down. Landmark F is located at 14 units across and 8 units down.

To find the horizontal distance, we can subtract the x-coordinates of the two landmarks:
14 - 5 = 9 units

To find the vertical distance, we can subtract the y-coordinates of the two landmarks:
8 - 9 = -1 unit

Since the vertical distance is negative, we can consider the absolute value of it:
|-1| = 1 unit

Using the Pythagorean theorem, we can calculate the distance between the two landmarks:

distance = √(horizontal distance)^2 + (vertical distance)^2
distance = √(9)^2 + (1)^2
distance = √81 + 1
distance = √82

Rounding to the nearest hundredth, the length between landmark B and F is approximately 9.06 units.

Answer 4

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

Answer 5

[AI-generated answer — Bot GPT 3.5]

To find the length of the diagonal of the rectangle, we can use the distance formula.

The two points that would form the diagonal of the rectangle are (-6, 8) and (4, -3).

Using the distance formula:

distance = √((x2 - x1)^2 + (y2 - y1)^2)

Substituting the coordinates of the two points:

distance = √((4 - (-6))^2 + (-3 - 8)^2)
distance = √((10)^2 + (-11)^2)
distance = √(100 + 121)
distance = √221

Rounding to the nearest hundredth, the length of the diagonal of the rectangle is approximately 14.87 units.

Answer 6

Find the distance between (2, 3) and (−4, −9). Round your answer to the nearest hundredth, if necessary.(1 point)

units

Answer 7

[AI-generated answer — Bot GPT 3.5]

To find the distance between (2, 3) and (-4, -9), we can use the distance formula.

The distance formula is given by:

distance = √((x2 - x1)^2 + (y2 - y1)^2)

Substituting the coordinates of the two points:

distance = √((-4 -2)^2 + (-9 -3)^2)
distance = √((-6)^2 + (-12)^2)
distance = √(36 + 144)
distance = √180

Rounding to the nearest hundredth, the distance between (2, 3) and (-4, -9) is approximately 13.42 units.

Answer 8

Find the distance between (−8, −3) and (−2, −5). Round your answer to the nearest hundredth, if necessary.(1 point)

units

Answer 9

[AI-generated answer — Bot GPT 3.5]

To find the distance between (-8, -3) and (-2, -5), we can use the distance formula.

The distance formula is given by:

distance = √((x2 - x1)^2 + (y2 - y1)^2)

Substituting the coordinates of the two points:

distance = √((-2 - (-8))^2 + (-5 - (-3))^2)
distance = √((6)^2 + (-2)^2)
distance = √(36 + 4)
distance = √40

Rounding to the nearest hundredth, the distance between (-8, -3) and (-2, -5) is approximately 6.32 units.