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Voronoi Diagrams

A variety of questions about Voronoi Diagrams presented in a self-marking, online exercise.
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This is level 1: general questions about a diagram of a rectangular shaped island. You can earn a trophy if you get at least 7 questions correct and you do this activity online.

Voronoi Diagram

This is a diagram of Oblong Island which, amazingly, is in the shape of a rectangle. Any location on the island can be defined by a set of coordinates.

There are seven camping sites on the island labelled A to G.

1. What are the coordinates of site C ? [Type in your answer as two numbers separated by a comma]

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2. What are the coordinates of site B ?

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3. A hiker finds themself at the point (2,3) at sunset. Which is the nearest campsite to that location?

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4. Which is the nearest site to (5,3)?

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5. Which is the nearest site to (2.4,2.1)?

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6. What are the coordinates of the midpoint of the line joining sites F and E?

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7. What are the coordinates of the point that is exactly the same distance (equidistant) from sites A, B and G?

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8. What are the y-coordinates of all the points on the edge equidistant from sites D and E?

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9. Each of the coloured regions in the diagram is called a cell. Each cell shows all of the locations that are closer to the site it containes than to any other site.

The units on the axes represent kilometers. Find the area, in square kilometers, of the cell containing site E.

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10. Multiple choice: which one of the following statements is true? Type the letter of the true statement:

A. The point (1,1) is equidistant from sites G and F.
B. The point (2,2) is closer to F than it is to G.
C. The point (3,3) is closer to site D than to any other site.
D. The site D is further from E than the site E is from F.
E. The sites A, B and D lie in a straight line.

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Check

This is Voronoi Diagrams level 1. You can also try:
Level 2 Level 3 Level 4

Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.
Why am I learning this?

Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

Comment recorded on the 24 May 'Starter of the Day' page by Ruth Seward, Hagley Park Sports College:

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"I think these are great! So useful and handy, the children love them.
Could we have some on angles too please?"

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Description of Levels

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Perpendicular Bisector - A step-by-step guide showing how to construct the perpendicular bisector of a line segment. This skill can then be used to construct a Voronoi Diagram.

Printable Worksheet: Get a real 'feel' for Voronoi diagrams with this resource on which you can draw Voronoi diagrams using the good, old-fashioned compasses, pencil and ruler method.

Level 1 - General questions about a diagram of a rectangular shaped island.

Level 2 - Questions involving the vocabulary and mathematics of Voronoi diagrams.

Level 3 - Find the coordinates of the missing sites in ten Voronoi Diagrams.

Level 4 - Define a region on a Voronoi Diagrams by finding the equations of the edges.

Exam Style Questions - A collection of problems in the style of IB exam paper questions.

More on Loci including lesson Starters, visual aids, investigations and self-marking exercises.

Voronoi move euclidean by Jahobr [CC0]

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

The video above is from Revision Village.

Definitions

Sites: These are the important locations from which the positions of the lines of the Voronoi diagram are calculated.

Cells: These are the areas that surround the sites and contain the points which are closer to that site than to any other site. The cells are labelled according to the site which they contain. They are also known as regions.

Edges: These are the borders between the cells. They are the lines showing the points equidistant from pairs of sites.

Vertices: A vertex is the point at which three or more edges meet. Each vertex is equally close to the sites whose cells meet at that vertex. They can also be called intersections.

Nearest Neighbour interpolation is a simple method of estimating the value of a variable at any point by using the variable's value at the nearest site.

Toxic Dump Problem: This problem can be described as finding the optimal position for a toxic waste dump, so as to maximise its distance from the nearest town. If not on the border of the diagram the location will always be at one of the vertices.

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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