2025 Beatty Sec 3 EOY Q13

2025 Beatty Sec 3 EOY Q13

Secondary 3
10 marks

The diagram shows a trapezium \(ABCD\) in which \(A(3,8)\), \(B(1,2)\) and \(C(5,4)\), angle \(BAD=90^\circ\) and \(BA\) is parallel to \(CD\).

  1. Show that the coordinates of \(D\) are \((6,7)\).[5]
  2. The point \(E\) lies on \(AC\) such that \(AE=3EC\). Given \(E(p,5)\), show that \(p=4.5\).[1]
  3. The point \(F\) lies on the \(x\)-axis such that \(FE\) is parallel to \(CD\). Find the coordinates of \(F\).[2]
  4. Hence, or otherwise, find the area of \(CDEF\).[2]

Solution:

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Answer:(a) \(D=(6,7)\); (b) \(p=4.5\); (c) \(F=\left(\dfrac{17}6,0\right)\); (d) \(\dfrac{10}3\text{ units}^2\).

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