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.

What is the shortest distance between the Science Lab and the Hostel models?

Correct Answer: The correct option is 50-inch.

Step-by-Step Explanation:

To find the shortest distance between the Science Lab and the Hostel models, let us establish a 2D Cartesian coordinate system with the Admin Building at the origin (0, 0).

Let East be the +x direction, West be the -x direction, North be the +y direction, and South be the -y direction.

1. Position of Admin Building:

$\text{Admin Building}=(0,0)$

2. Position of Science Lab:
The Admin Building is 50 inches to the west of the Science Lab. This means the Science Lab is 50 inches to the east of the Admin Building.

$\text{Science Lab}=(50,0)$

3. Position of Sports Center:
The Science Lab is 40 inches to the north of the Sports Center. Therefore, the Sports Center is 40 inches to the south of the Science Lab.

$\text{Sports Center}=(50,0-40)=(50,-40)$

4. Position of Hostel:
The Hostel is 30 inches to the west of the Sports Center.

$\text{Hostel}=(50-30,-40)=(20,-40)$

5. Calculating the Shortest Distance between Science Lab and Hostel:
Coordinates of Science Lab: (50, 0)
Coordinates of Hostel: (20, -40)

Using the distance formula $d=\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$:

$d=\sqrt{{(50-20)}^2+{(0-(-40\left)\right)}^2}$

$d=\sqrt{{30}^2+{40}^2}$

$d=\sqrt{900+1600}$

$d=\sqrt{2500}=50\text{inches}$

Thus, the shortest distance between the Science Lab and the Hostel models is 50-inch.