Question

The following three points are the locations of important facilities in a transportation network: (23,13),(55,63), and (41,46). The coordinates are in miles. a. Calculate the Euclidean distances (in miles) between each of the three pairs of facilities. (Enter your responses rounded to two decimal places.)

Answer 1

The Euclidean distances between the three pairs of facilities are approximately 59.37 miles, 37.58 miles, and 22.02 miles, calculated using the distance formula.

Step-by-step explanation:

The calculation of the Euclidean distances between points involves using the distance formula based on Pythagorean Theorem, d = √((x2-x1)² + (y2-y1)²), where (x1, y1) and (x2, y2) are the coordinates of two points.

To calculate the Euclidean distance between the three pairs of facilities located at (23,13),(55,63), and (41,46), we will apply the distance formula for each pair:

• The distance between (23,13) and (55,63) is √((55-23)² + (63-13)²) = √(1024 + 2500) = √3524 ≈ 59.37 miles.
• The distance between (23,13) and (41,46) is √((41-23)² + (46-13)²) = √(324 + 1089) = √1413 ≈ 37.58 miles.
• The distance between (55,63) and (41,46) is √((55-41)² + (63-46)²) = √(196 + 289) = √485 ≈ 22.02 miles.

These calculations provide the distances required for the transportation network analysis.