IB SL Voronoi diagrams - complete study guide with answers. 10 page complete summary

Voronoi diagrams


Warm – up:

Exercise 1:

Write down the equation of each of these lines:




Exercise 2:

Work out the midpoint of the following coordinates:




Exercise 3:

M is the midpoint of PQ

Find the coordinates of Q

,Voronoi diagrams


Exercise 4:

Work out the equation of a line which passes through A(1,4) and B(5,16)




Work out an equation of a line which is parallel to AB, but passes though C(1,7)




Work out the midpoint of AB




Work out an equation of a line perpendicular to AB which passes through the midpoint of AB

,Voronoi diagrams


Theory Recap:

On these diagrams label: site, cell, circumcircle, vertex, edge, Voronoi cell, circumcentre




Exercise 5:

Using this Voronoi diagram, determine which cell each coordinate belongs to:



(2, 3)

(6, 5)

(2.5, 3.5)

(7, 6)

(4, 2)

, Voronoi diagrams


Exercise 6: Perpendicular bisectors

Complete the table below and draw the perpendicular bisectors for each of the line
segments on the graph below. The bisector for line 𝐴𝐵̅̅ has already been drawn.




Line AB: Worked example Line AD
Midpoint: Midpoint:
Gradient: Gradient:

Perpendicular Gradient: Perpendicular Gradient:
Perp. Line equation: Perp. Line equation:
Line BC Line CD
Midpoint: Midpoint:
Gradient: Gradient:
Perpendicular Gradient:
Perpendicular Gradient: Perp. Line equation:
Perp. Line equation:
Line CD Empty cell :)
Midpoint:
Gradient:

Perpendicular Gradient:
Perp. Line equation: