2026 CSS P2 Q8

2026 CSS P2 Q8

Secondary 4
12 marks
  1. The position vector of point \(X\) is \(\begin{pmatrix}8 \\ -4\end{pmatrix}\).
    The position vector of point \(Y\) is \(\begin{pmatrix}6 \\ 4\end{pmatrix}\).
    1. Find the vector that represents the translation from \(X\) to \(Y\).[1]
    2. Find the magnitude of \(\overrightarrow{XY}\).[2]
    3. \(Z\) has coordinates \((-1,k)\) and lies on the line \(XY\) produced.
      Find the position vector of point \(Z\).[2]
  2. In the diagram, \(\overrightarrow{AB}=4\mathbf a\), \(\overrightarrow{AD}=8\mathbf b\) and \(\overrightarrow{EF}=2(\mathbf a-\mathbf b)\).
    \(E\) is the point on \(BD\) such that \(BE:BD=3:4\).
    \(F\) is the midpoint of \(BC\).
    1. Express \(\overrightarrow{BE}\) in terms of \(\mathbf a\) and \(\mathbf b\), as simply as possible.[2]
    2. Express \(\overrightarrow{BC}\) in terms of \(\mathbf a\) and \(\mathbf b\), as simply as possible.[2]
    3. What type of quadrilateral is \(ABCD\)? Justify your answer using vectors.[3]

Solution:

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Answer:(a)(i) \(\begin{pmatrix}-2 \\ 8\end{pmatrix}\) (ii) \(2\sqrt{17}\approx8.25\) units (iii) \(\begin{pmatrix}-1 \\ 32\end{pmatrix}\) (b)(i) \(6\mathbf b-3\mathbf a\) (ii) \(8\mathbf b-2\mathbf a\) (iii) Trapezium, since \(\overrightarrow{AB}=2\overrightarrow{DC}\).

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