IB Mathematics Applications & Interpretation Topic SL 3.6—voronoi Diagrams Questionbank (SL/HL)

IB Mathematics Applications & Interpretation Topic SL 3.6—voronoi Diagrams Questionbank (SL/HL) | RevisionDojo

Practice IB Mathematics Applications & Interpretation (AI) Topic SL 3.6—voronoi Diagrams with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for SL 3.6—voronoi Diagrams and mirrors Paper 1, 2, 3 style where relevant.

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Paper

Level

Question 1

SL & HLPaper 2

The Voronoi diagram shows three sites

A (0, 0)

B (6, 2)

, and

C (2, 6)

. The boundaries between the cells are the perpendicular bisectors of the segments

[A B]

[A C]

, and

[B C]

Find the equation of the perpendicular bisector of $[A B]$ , giving your answer in the form $y = m x + c$ .

[4]

Find the equation of the perpendicular bisector of $[A C]$ , giving your answer in the form $y = m x + c$ .

[4]

Find the coordinates of the Voronoi vertex.

[2]

Verify that the Voronoi vertex is equidistant from all three sites by computing one such distance.

[2]

Question 2

SL & HLPaper 1

The Voronoi diagram shows the locations of

5

sites:

A (0, 4)

B (8, 4)

C (4, 0)

D (4, 8)

, and

E (4, 4)

Write down the coordinates of the four vertices of the cell of site $E$ .

[2]

Hence find the area of the cell of site $E$ .

[3]

Question 3

SLPaper 1

Consider an edge of a Voronoi diagram. Site $P$ is located at $(1, 8)$ . The edge $m$ , which acts as the perpendicular bisector between sites $P$ and $Q$ , is defined by the linear equation $y = 2 x + 1$ . Determine the coordinates of site $Q$ .

Determine the coordinates of site $Q$ .

[5]

Question 4

SLPaper 1

The diagram below shows a Voronoi diagram formed by five points:

A (0, 2)

B (6, 2)

C (6, 6)

D (0, 6)

, and

E (3, 4)

. Each region corresponds to the area closest to one of the points.

Which region corresponds to point $C$ ?

[1]

Find the equation of the perpendicular bisector used to separate the regions of $A$ and $B$ .

[2]

Question 5

SL & HLPaper 1

Two sites

A

and

B

are placed at

A (2, 3)

and

B (8, 7)

. A point

P (9, 2)

is marked on the diagram.

Find the equation of the perpendicular bisector of $[A B]$ , giving your answer in the form $a x + b y + d = 0$ , where $a$ , $b$ , $d \in Z$ .

[4]

Hence determine which of the sites, $A$ or $B$ , lies closer to the point $P$ . Justify your answer.

[3]

IB Mathematics Applications & Interpretation SL 3.6—voronoi Diagrams Questionbank

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IB Mathematics Applications & Interpretation SL 3.6—voronoi Diagrams Questionbank

IB Mathematics Applications & Interpretation (AI) Topic SL 3.6—voronoi Diagrams Questionbank

Unlock all 18 questions with a free account