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.

Question

Find the length between landmark A
and landmark E
.

(1 point)

Answer 1

To find the length between landmark A (the White House) and landmark E (the National Portrait Gallery), we can use the distance formula for points on a grid.

The coordinates for the landmarks are as follows:

• Point A (White House): (4, 3)
• Point E (National Portrait Gallery): (12, 3)

Since both points share the same y-coordinate (3), the distance between these two points can be calculated by finding the difference in their x-coordinates:

\[ \text{Distance} = |x_2 - x_1| = |12 - 4| = 8 \text{ units} \]

Considering the scale provided (200 feet per unit), we can convert the distance to feet:

\[ \text{Distance in feet} = 8 \text{ units} \times 200 \text{ feet/unit} = 1600 \text{ feet} \]

Thus, the length between landmark A and landmark E is 1600 feet.