To find the distance between landmarks B (the Washington Monument) and F (the National Gallery of Art) on the grid, we will use the distance formula.
The coordinates of the points are as follows:
- Point B: (5 units across, 9 units down)
- Point F: (14 units across, 8 units down)
First, we can calculate the difference in x-coordinates and y-coordinates:
\[ \Delta x = x_F - x_B = 14 - 5 = 9 \text{ units} \]
\[ \Delta y = y_F - y_B = 8 - 9 = -1 \text{ unit} \]
Next, we apply the distance formula:
\[ d = \sqrt{(\Delta x)^2 + (\Delta y)^2} \]
Substituting the values we calculated:
\[ d = \sqrt{(9)^2 + (-1)^2} = \sqrt{81 + 1} = \sqrt{82} \]
Now we can compute the square root of 82:
\[ d \approx 9.055 \]
According to the scale mentioned in the problem, if we consider the distance in feet or meters, we would need to clarify this, but since the problem asks for the distance in terms of the grid units, we will keep it as is.
Rounding to the nearest hundredth, the distance between point B and point F is approximately:
\[ \text{Distance} \approx 9.06 \text{ units} \]
Thus, the length between landmark B and F is approximately 9.06 units.