Read the following campus layout information carefully and answer the question that follows:

Eight miniature models of university facilities are placed on a display table at various distances from each other. The model of the Admin Building is 50 inches to the west of the Science Lab model. The Library model is 70 inches to the east of the Main Gate model. The Hostel model is 20 inches to the north of the Dining Hall model, which is 30 inches to the west of the Parking Lot model. The Admin Building model is 40 inches to the south of the Main Gate model. The Science Lab model is 40 inches to the north of the Sports Center model. The Hostel model is 30 inches to the west of the Sports Center model.

In which direction is the Admin Building model with respect to the Dining Hall model?

The correct answer is North-west.

Step-by-Step Explanation:

Let us determine the relative coordinates of each facility by setting the Admin Building as the origin (0, 0), where North is the +y direction, South is the -y direction, East is the +x direction, and West is the -x direction.

1. Position of Admin Building:
Let Admin Building = (0, 0).

2. Position of Science Lab:
The Admin Building is 50 inches to the west of the Science Lab.
Therefore, Science Lab is 50 inches to the east of the Admin Building.
Science Lab = (50, 0).

3. Position of Main Gate:
The Admin Building is 40 inches to the south of the Main Gate.
Therefore, Main Gate is 40 inches to the north of the Admin Building.
Main Gate = (0, 40).

4. Position of Sports Center:
The Science Lab is 40 inches to the north of the Sports Center.
Therefore, Sports Center is 40 inches to the south of the Science Lab.
Sports Center = (50, -40).

5. Position of Hostel:
The Hostel is 30 inches to the west of the Sports Center.
Hostel = (50 - 30, -40) = (20, -40).

6. Position of Dining Hall:
The Hostel is 20 inches to the north of the Dining Hall.
Therefore, Dining Hall is 20 inches to the south of the Hostel.
Dining Hall = (20, -40 - 20) = (20, -60).

7. Finding the direction of Admin Building with respect to Dining Hall:
Admin Building coordinate = (0, 0)
Dining Hall coordinate = (20, -60)

To go from the Dining Hall (20, -60) to the Admin Building (0, 0):
- We must move 20 inches to the West (from x = 20 to x = 0).
- We must move 60 inches to the North (from y = -60 to y = 0).

Combining North and West gives North-west. Thus, the Admin Building model is in the North-west direction with respect to the Dining Hall model.