2025 Paradigm Sec 3 Mock EOY Q12

2025 Paradigm Sec 3 Mock EOY Q12

Secondary 3
11 marks

[Coordinate Geometry]

\(ABCD\) is a trapezium such that the coordinates of \(A\) and \(C\) are \((6,1)\) and \((-5,4)\) respectively. Angles \(ADC\) and \(BCD\) are right angles and the gradient of \(AB\) is \(-\dfrac43\).

  1. Show that the coordinates of \(B\) are \((0,9)\).[2]
  2. Show that the coordinates of \(D\) are \((2,-3)\).[4]
  3. Find the area of triangle \(ABD\).[2]
  4. Find angle \(ABC\).[3]

Solution:

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Answer:(i) \(B=(0,9)\); (ii) \(D=(2,-3)\); (iii) \(28\text{ units}^2\); (iv) \(81.9^\circ\).

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