Question

Calculate both the rectilinear and Euclidean distances separating the three existing facilities located at (5, 15), (10, 20), and (6, 9) within the coordinate system imposed on a map.

Answer 1

To calculate the rectilinear distance, find the sum of the absolute differences of the x-coordinates and y-coordinates. To calculate the Euclidean distance, use the distance formula: sqrt((x2 - x1)^2 + (y2 - y1)^2).

Step-by-step explanation:

To calculate the rectilinear distance, we need to find the sum of the absolute differences of the x-coordinates and y-coordinates of each pair of points. For example, for the first pair of points (5, 15) and (10, 20), the rectilinear distance would be |5 - 10| + |15 - 20| = 5 + 5 = 10. Similarly, for the second pair of points (10, 20) and (6, 9), the rectilinear distance would be |10 - 6| + |20 - 9| = 4 + 11 = 15.

To calculate the Euclidean distance, we need to use the distance formula: sqrt((x2 - x1)^2 + (y2 - y1)^2). Using this formula, the Euclidean distance between the first pair of points would be sqrt((10 - 5)^2 + (20 - 15)^2) = sqrt(25 + 25) = sqrt(50). Similarly, the Euclidean distance between the second pair of points would be sqrt((6 - 10)^2 + (9 - 20)^2) = sqrt(16 + 121) = sqrt(137).