2025 IGCSE 0580 February/March P42 Q8

2025 IGCSE 0580 February/March P42 Q8

5 marks

The scale drawing shows the positions of boat \(A\) and boat \(B\).

The scale is \(1\text{ cm}\) represents \(0.5\text{ km}\).

  1. Find the actual distance between boat \(A\) and boat \(B\).[2]
  2. Lighthouse \(L\) lies to the east of boats \(A\) and \(B\).
    \(L\) is \(4.4\text{ km}\) from boat \(A\) and \(3.3\text{ km}\) from boat \(B\).
    Using a ruler and compasses only, construct and label the position of \(L\).[3]

Solution:

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Answer:(a) \(2.1\text{ km}\). (b) The eastern intersection of arcs centred at \(A\), radius \(8.8\text{ cm}\), and \(B\), radius \(6.6\text{ cm}\).

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