[color=#ff0000][center][b]Emergency Zone Crisis[/b][/center][br][/color]The mayor of Geometry City needs your help! Four critical locations are competing for funding based on their service coverage:[list=1][*]Hospital (H) at [i][math](1,4)[/math][/i][/*][*]Fire Station (F) at [i][math](5,6)[/math][/i][/*][*]Police Station (P) at [i][math](3,1)[/math][/i][/*][*]School (S) at [i][math](7,3)[/math][/i][/*][/list]Disaster Strikes! A flood has hit at point [i][math](4,4)[/math][/i]. Only the nearest service can respond due to budget cuts.
[b][i]Task-1[/i][/b][br][br]Calculate the distances of flood point to all the locations.
Distance of H to flood point.
Distance of F to flood point.
Distance of P to flood point.
Distance of S to flood point.
[b][i]Task-2[/i][/b][br][br]Decide the closest loaction
What if the flood center point is at [math](5,4)[/math]?
Closest Location from [math](5,4)[/math] is
Use the interactive applet above to drag the flood point (💧) to new positions.[br]Find and mark 2 distinct points where the Fire Station (F) is the closest facility and Justify your choices.[br]
Manually calculating distances for every [color=#ff0000]emergency[/color] would be time-consuming and inefficient. To solve this, click the [b]'Hint'[/b] button in the interactive applet. This will reveal the pre-divided service regions - showing exactly which facility is closest to any point in the city![br]
[i]Notice how the boundaries between regions are special lines - what do you [b]observe[/b] about their angles and positions relative to the service points? [br][/i]
[i]The concept used to solve the problem: [br][br]A [b]Voronoi diagram[/b] divides a space into distinct regions (called "cells") around a set of predefined points (called "sites"). Each cell consists of all locations that are closer to its site than to any other site. The boundaries between cells are formed by perpendicular bisectors of the lines connecting neighboring sites.[/i]