Free Voronoi diagrams questions for IB Mathematics: Applications & Interpretation (SL & HL), part of Geometry & trigonometry. Each question has the answer and the marking points an examiner would look for.
Generate a full Voronoi Diagrams worksheet →All Geometry & trigonometry questionsThree schools are located at P(0, 8), Q(2, 8) and R(6, 6). A new library is to be built at the point that is the same distance from all three schools.
Find the coordinates of the library and its distance from each school.
| Part | Answer and marking points | Marks |
|---|---|---|
| (1, 1); 7.07 perpendicular bisector of one pair of schools M1 a second perpendicular bisector M1 correct equations A1A1 (1, 1) A1 distance 7.07 A1 | 6 |
Two mobile phone masts are at A(3, 3) and B(5, 9). A phone connects to the nearest mast.
Find the equation of the perpendicular bisector of AB, giving your answer in the form y = mx + c.
A phone is at P(3, 5). Determine which mast it connects to.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | y = −13x + 223 midpoint (4, 6) A1 gradient of AB = 3 A1 perpendicular gradient −13 (M1) y = −13x + 223 A1 | 4 |
| (b) | A PA = 2.00, PB = 4.47 (M1) A A1 | 2 |
Three post offices are at A(0, 0), B(4, 0) and C(0, 4).
Find the equations of the perpendicular bisectors of AB and AC.
Find the coordinates of the vertex of the Voronoi diagram, and explain its significance.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | x = 2; y = 2 x = 2 A1 y = 2 A1 | 2 |
| (b) | (2, 2) (2, 2) A1 equidistant from all three post offices R1 | 2 |
Three schools are located at P(6, 6), Q(0, 8) and R(4, 8). A new library is to be built at the point that is the same distance from all three schools.
Find the coordinates of the library and its distance from each school.
| Part | Answer and marking points | Marks |
|---|---|---|
| (2, 4); 4.47 perpendicular bisector of one pair of schools M1 a second perpendicular bisector M1 correct equations A1A1 (2, 4) A1 distance 4.47 A1 | 6 |
Two mobile phone masts are at A(2, 1) and B(6, 7). A phone connects to the nearest mast.
Find the equation of the perpendicular bisector of AB, giving your answer in the form y = mx + c.
A phone is at P(2, 8). Determine which mast it connects to.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | y = −23x + 203 midpoint (4, 4) A1 gradient of AB = 32 A1 perpendicular gradient −23 (M1) y = −23x + 203 A1 | 4 |
| (b) | B PA = 7.00, PB = 4.12 (M1) B A1 | 2 |
Three post offices are at A(0, 0), B(6, 0) and C(0, 4).
Find the equations of the perpendicular bisectors of AB and AC.
Find the coordinates of the vertex of the Voronoi diagram, and explain its significance.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | x = 3; y = 2 x = 3 A1 y = 2 A1 | 2 |
| (b) | (3, 2) (3, 2) A1 equidistant from all three post offices R1 | 2 |
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Meet Riyaz →Original IB-style practice questions written for mentorriyaz.in. These are not IB past paper questions, and this site is not affiliated with or endorsed by the International Baccalaureate Organization. Updated 2026-11-04. Paper generator · mentorriyaz.in