# im.g.1.9.3.Now Who is Closest?

- Author:
- mark vasicek

## Instructions

This image of the fire departments in Des Moines County, Iowa was imported into GeoGebra using the Image tool.
1. Create points at each of the three stations.
We want to use the Voronoi function, named after Georgy Voronoi, the 19th century Ukranian mathematician who invented it. To do this, first we need to create a "list" of the points that are to be diagramed.
2. In the Input Bar (next to the "+" sign) type: List1={C,D,E} You start with point C because when the image was imported, it used points A and B. We do not want the Voronoi diagram to include those points.
3. In the Input Bar type: Voronoi(List1)

## Ready for More?

Below is an extension of what you did in the first application.
It follows the same type of procedure, however it deals with a more complicated situation.
It is a map of the Farmington, Connecticut fire department's Life Star landing sites.
Construct points for each of the landing sites on the map.
You can view the names of the points by selecting from the main 3 bars View=>Algebra.
This also displays the Input Bar (next to the "+" sign).
Again, points A and B were used to import the image using the Image tool. (Can you find the Image tool?)
Do not use points A and B in making a list of all the points.
To make the list type: List1={C,D, <... and here list all the other points that you created on the drawing>}
Oh yeah. One more thing. When you type the names of the points, the program uses capital block letters A-Z... You will run out of letters, so use A_1 etc... to write subscripts. And don't use X or Y or X_1 and Y_1 because those have special purposes. Good luck with this!
Finally, type: Voronoi(List1)

## Attribution

illustrative mathematics. geometry. unit 1. lesson 9. activity 3.
"Now Who is Closest?"
https://im.kendallhunt.com/HS/teachers/2/1/9/index.html
Licensed under the Creative Commons Attribution 4.0 license
https://creativecommons.org/licenses/by/4.0/
I added to the IM materials a simpler fire station map (only 3 points) in Burlington, Iowa, to practice the Voronoi function in GeoGebra with an easier task first.

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