EXM.1.SL.TZ0.4

pestleMathematicsAISLPaper 1EXM· sl-3-6-voronoi-diagramssource ↗

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 $y = - 2x + 9$

Find the co-ordinates of the point A.

Markscheme / solution

Line from A to B will have the form $y = \frac{1}{2}x + c$ M1A1

Through $\left( {4{\text{,}}\,\,6} \right) \Rightarrow c = 4$ so line is $y = \frac{1}{2}x + 4$ M1A1

Intersection of $y = - 2x + 9$ and $y = \frac{1}{2}x + 4$ is (2, 5) M1A1

Let $A = \left( {p{\text{,}}\,\,q} \right)$ then $\left( {2{\text{,}}\,\,5} \right) = \left( {\frac{{p + 4}}{2},\frac{{q + 6}}{2}} \right) \Rightarrow p = 0{\text{,}}\,\,q = 4$ M1A1A1

$A = \left( {0,4} \right)$

[9 marks]

Examiners’ report

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