2025 AISS PRELIMS P1 Q7

2025 AISS PRELIMS P1 Q7

Secondary 4
8 marks
2025 Ahmad Ibrahim Secondary School Prelims A Math Paper 1

The diagram shows an isosceles triangle \(ABC\) in which \(A(-3,0)\), \(B\left(\dfrac{1}{2},3\right)\) and \(C(5,2)\). \(M\) is the foot of perpendicular from \(B\) to \(AC\).

  1. Find the coordinates of \(M\).[1]
  2. Find the equation of the perpendicular bisector of \(AC\).[2]
  3. Given that \(ABCD\) is a kite with \(BM=\dfrac{2}{7}BD\), find the coordinates of \(D\).[3]
  4. Find the area of the kite \(ABCD\).[2]

Solution:

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Answer:(a) \(M=(1,1)\) (b) \(y=-4x+5\) (c) \(D=\left(\dfrac{9}{4},-4\right)\) (d) \(\dfrac{119}{4}\text{ units}^2\)

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