Apps. and Interpretation for IBDP Maths Ebook 1 | Page 127

3. The positions of three schools A , B and C in a rectangular coordinate plane are at
(4, 2), (2, 4) and (6, 4) respectively. Anna is applying a school for her son. She wants to
find a school which is closest to her house. The position of her home is at (4.15, 4) .
(a) (i) Find the distance between her home and the school A .
(ii) Write down the distance between her home and the school B .
(b)
(iii) Write down the distance between her home and the school C .
Write down the school in which Anna is going to apply for her son.
[4]
[1]
4. The positions of two fire stations A and B in a rectangular coordinate plane are at
(2.5, 2.5) and (7.5, 7.5) respectively.
(a) Find the coordinates of the mid-point of AB .
A building is located at a point on the line segment AB .
[2]
(b) Write down the range of the x -coordinates of the position of the building if it lies
in the Voronoi cell of the fire station A .
[1]
A park is located at (5.5, 6.5).
(c) Show that the park lies in the Voronoi cell of the fire station B .
[3]
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