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Vectors - Ratio Theorem and Section Formula

Vectors - Ratio Theorem and Section Formula

Secondary 3

In the diagram, \(ABCD\) is a trapezium with \(BC\) has a length of \(6\) units.

The coordinates of \(A\) and \(B\) are \((-4, 0)\) and \((1, 4)\) respectively.

The area of the trapezium is \(48\) square units.

  1. Calculate
    1. the coordinates of \(C\),
    2. the length of \(AB\),
    3. the equation of \(AB\),
    4. the coordinates of \(D\).
  2. The point \(E\) is on \(AB\) produced such that \(BE = 2AB\). Calculate the coordinates of \(E\).

Solution:

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Answer:(a)(i) \(C=(7,4)\) (ii) \(AB=\sqrt{41}\) units, approximately \(6.40\) units (iii) \(y=\dfrac45x+\dfrac{16}{5}\) (iv) \(D=(14,0)\) (b) \(E=(11,12)\).

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