To find the distance between landmarks B (Washington Monument) and F (National Gallery of Art), we can use the distance formula for two points in a grid:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Where \((x_1, y_1)\) are the coordinates of point B and \((x_2, y_2)\) are the coordinates of point F.
The coordinates for the points are as follows:
- Point B (Washington Monument): (5, 9)
- Point F (National Gallery of Art): (14, 8)
Plugging the coordinates into the distance formula:
\[ d = \sqrt{(14 - 5)^2 + (8 - 9)^2} \] \[ d = \sqrt{(9)^2 + (-1)^2} \] \[ d = \sqrt{81 + 1} \] \[ d = \sqrt{82} \] \[ d \approx 9.055 \]
Now, if the scale is 200 feet and 200 meters, we need to determine the actual distance in either feet or meters.
Since the grid suggests each unit represents a fixed distance, we'll proceed to calculate the actual distance based on the grid units. The interpretation of the scale "200 feet and 200 meters" implies we lack specific unit conversion information. However, rounding the distance found:
So we round 9.055 to the nearest hundredth:
\[ \text{Rounded Distance} \approx 9.06 \text{ units} \]
Thus, the distance between landmark B and F is approximately 9.06 units in the context of the grid, utilizing the map's scale to interpret real-world distances depends on further context.