2025 SCGS PRELIMS P2 Q11
2025 SCGS PRELIMS P2 Q11
Secondary 4
11 marks
The diagram shows a trapezium with vertices \(A(6, 8)\), \(B\), \(C\) and \(D\). The sides \(AB\) and \(DC\) are parallel and angle \(ABC\) is \(90^\circ\). \(AB\) passes through the origin \(O\) and the length of \(AB\) is 15 units. The points \(C\) and \(D\) lie on the \(y\)-axis and \(x\)-axis respectively.
- Show that the coordinates of \(B\) are \((-3, -4)\).[4]
- Find the coordinates of \(C\) and of \(D\).[5]
- Find the area of the trapezium \(ABCD\).[2]
Solution:
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Answer:(a) \(B=(-3,-4)\) (b) \(C=\left(0,-\frac{25}{4}\right),\ D=\left(\frac{75}{16},0\right)\) (c) \(\frac{5475}{128}\text{ units}^2\)
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