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Date May Example question Marks available 9 Reference code EXM.1.SL.TZ0.4
Level Standard Level Paper Paper 1 Time zone Time zone 0
Command term Find Question number 4 Adapted from N/A

Question

The diagram below is part of a Voronoi diagram.

Diagram not to scale

A and B are sites with B having the co-ordinates of (4, 6). L is an edge; the equation of this perpendicular bisector of the line segment from A to B is y=2x+9y=2x+9

Find the co-ordinates of the point A.

Markscheme

Line from A to B will have the form y=12x+cy=12x+c      M1A1

Through (4,6)c=4(4,6)c=4   so line is y=12x+4y=12x+4      M1A1

Intersection of y=2x+9y=2x+9 and y=12x+4y=12x+4 is (2, 5)      M1A1

Let A=(p,q)A=(p,q) then (2,5)=(p+42,q+62)p=0,q=4(2,5)=(p+42,q+62)p=0,q=4      M1A1A1

A=(0,4)A=(0,4) 

[9 marks]

Examiners report

[N/A]

Syllabus sections

Topic 3—Geometry and trigonometry » SL 3.6—Voronoi diagrams
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Topic 3—Geometry and trigonometry

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