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Question 4

From Math Applications HL Paper 1 (May 2025, TZ2)

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  1. [Maximum mark: 7]

Consider the Voronoi diagram which shows the sites A(3, 3), B(10, 5), C(7, 2), D(5, 9), E(1, 5) and F(6, 5). The diagram also shows the cells formed by each site and their boundaries.

A Voronoi diagram showing points A, B, C, D, E, F and the regions (cells) around them, with grid lines and axes labeled x and y.
A Voronoi diagram showing points A, B, C, D, E, F and the regions (cells) around them, with grid lines and axes labeled x and y.

Vertex X is equidistant from sites B, C and F.

(a) (i) Write down the coordinates of X.

(ii) The exact value of BX is n\sqrt{n}. Write down the value of n. [2]

Vertex Y(a, b) is equidistant from sites B, D and F.

(b) (i) Write down the value of a.

(ii) Find the exact value of b. [5]