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1. [Maximum mark: 14]

Mai is at an amusement park. A map of part of the amusement park is represented on the following coordinate axes.

Mai’s favourite three attractions are positioned at A(0, 16), B(12, 20) and C(12, 0).
All measurements are in metres.

(a) Write down the distance between B and C. [1]

(b) Calculate the distance between A and B. [2]

(Question 1 continued)

Mai is standing at the attraction at B and wants to walk directly to the attraction at A.

(c) Calculate the bearing of A from B. [3]

A drinking fountain is to be installed at a point that is an equal distance from each of the attractions at A, B and C.

(d) (i) Write down the gradient of $AC$.

(ii) Write down the mid‑point of $AC$.

(iii) Hence calculate the coordinates of the drinking fountain. [8]