2026 NORTHBROOKS P2 Q8

2026 NORTHBROOKS P2 Q8

Secondary 4
7 marks

In the diagram, \(P,Q\) and \(R\) are vertices of a triangle with coordinates of \(P(-5,8)\), \(Q(7,-1)\) and \(R(k,-6)\). The length of line \(QR\) is 13 units.

  1. Find the value of \(k\).[2]
  2. Find the area of triangle \(PQR\).[2]
  3. Find the equation of the line \(PQ\).[3]

Solution:

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Answer:(a) \(k=-5\). (b) \(84\text{ units}^2\). (c) \(y=-\dfrac34x+\dfrac{17}{4}\).

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