2025 PHS P2 Q9

2025 PHS P2 Q9

Secondary 4
8 marks

The points \(A\) and \(B\) have coordinates \((0,a)\) and \((4,0)\) respectively, where \(a>0\). The perpendicular bisector of \(AB\) crosses the line \(x=-1\) at \(C\).

  1. Show that the \(y\)-coordinate of \(C\) is \(\dfrac{a^2-24}{2a}\).[5]
  2. Given that the area of triangle \(ABC\) is \(7.5a\) square units, find the value of \(a\).[3]

Solution:

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Answer:(a) \(y_C=\dfrac{a^2-24}{2a}\) (shown). (b) \(a=2\).

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