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2026 NYGH P1 Q10

2026 NYGH P1 Q10

IP 4
11 marks

A logistics company is testing a drone delivery route in a smart city. The drone’s flight path is mapped on a coordinate grid, where each unit represents \(100\text{ m}\). Point \(A\) at coordinates \((-2,3)\) and point \(B\) at coordinates \((8.4,-6.1)\) are two delivery points.

  1. Find the actual distance \(AB\).[2]
  2. Find the equation of the line \(AB\).[2]
  3. Find the equation of the perpendicular bisector of \(AB\).[3]
  4. The drone starts from \(A\) and moves towards a point \(C\) such that \(C\) lies on the line \(AB\) and \(AB:BC=3:2\). Find the two possible coordinates of \(C\).[4]

Solution:

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Answer:(a) \(1.38\times10^3\text{ m}\) (b) \(y=-\dfrac78x+\dfrac54\) (c) \(y=\dfrac87x-\dfrac{729}{140}\) (d) \(\left(\dfrac{22}{15},-\dfrac1{30}\right)\) or \(\left(\dfrac{46}{3},-\dfrac{73}{6}\right)\).

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