Vector Properties of Parallelograms on a Square Grid
Vector Properties of Parallelograms on a Square Grid
Secondary 4
The \(1\) unit by \(1\) unit square grid below shows the positions of point \(A\), \(B\) and \(P\).
A coordinate grid showing the relative positions of points P, B, and A.
- Express \(\overrightarrow{AB}\) and \(\overrightarrow{PB}\) as column vectors.
- \(Q\) is a point such that \(ABQP\) is a parallelogram. Express \(\overrightarrow{BQ}\) as a column vector.
- \(R\) is a point such that \(ABPR\) is a parallelogram. Express \(\overrightarrow{BR}\) as a column vector.
- Do the two vectors \(\overrightarrow{PQ}\) and \(\overrightarrow{PR}\) have the same magnitude? Is \(\overrightarrow{PQ} = \overrightarrow{PR}\)? Explain.
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Answer:(i) \(\overrightarrow{AB}=\begin{pmatrix}-5\\-3\end{pmatrix}\), \(\overrightarrow{PB}=\begin{pmatrix}1\\-5\end{pmatrix}\) (ii) \(\overrightarrow{BQ}=\begin{pmatrix}-6\\2\end{pmatrix}\) (iii) \(\overrightarrow{BR}=\begin{pmatrix}4\\8\end{pmatrix}\) (iv) Same magnitude \(\sqrt{34}\), but \(\overrightarrow{PR}=-\overrightarrow{PQ}\)
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