VORONOI DIAGRAMS I

A Voronoi diagram in one which displays

‘zones of proximity’ – as you go through

this activity you will learn what that means.

ACTIVITY I

Suppose A and B on the grid above represent two towns ?

Is point C closer to A or B ? ______            Is point D closer to A or B ? ______

Is point E closer to A or B ? ______            Is point F closer to A or B ? ______

Use the length formula to calculate all the lengths to confirm your answers.

A second method to determine which point is closest to which town is the following.

Draw a line joining A and B.

Calculate the coordinates of the midpoint of AB :

Calculate the slope of AB :

Calculate the slope of a line perpendicular to AB :

Draw in that perpendicular line, passing through the midpoint of AB.

That line, the perpendicular bisector of AB, divides the grid into two regions.

All the points to the left of the line are closer to A than B, all points to the right closer to B.

This is a simple Voronoi diagram.