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?

The correct answer is 50-inch.

Step-by-Step Explanation:

To find the shortest (straight-line) distance between the Science Lab and the Hostel models, we can determine their positions relative to a common reference point using Cartesian coordinates (where East-West represents the horizontal X-axis and North-South represents the vertical Y-axis).

Let us choose the position of the Sports Center model as our reference origin point (0, 0):

1. Position of Science Lab model:
It is given that the Science Lab model is 40 inches to the north of the Sports Center model.
Therefore, its coordinates are (0, 40).

2. Position of Hostel model:
It is given that the Hostel model is 30 inches to the west of the Sports Center model.
Therefore, its coordinates are (-30, 0).

3. Calculating the shortest distance between Science Lab and Hostel:
The horizontal separation (difference in X-coordinates) is:
$\mathrm{\Delta x}=0-(-30)=30\text{inches}$
The vertical separation (difference in Y-coordinates) is:
$\mathrm{\Delta y}=40-0=40\text{inches}$

Using the distance formula derived from the Pythagorean theorem:

$\text{Distance}=\sqrt{{\left(\mathrm{\Delta x}\right)}^2+{\left(\mathrm{\Delta y}\right)}^2}$

Substituting the values into the formula:

$\text{Distance}=\sqrt{{30}^2+{40}^2}$

$\text{Distance}=\sqrt{900+1600}$

$\text{Distance}=\sqrt{2500}$

$\text{Distance}=50\text{inches}$

Thus, the shortest distance between the Science Lab model and the Hostel model is 50 inches.