Vertices of a parallelogram from two sides
Vertices of a parallelogram from two sides
Secondary 4
5 marks
In parallelogram \(KLMN\), the vertex \(K\) is the point \((-2,\ 1)\), \(\overrightarrow{KL}=\begin{pmatrix}5\\ 3\end{pmatrix}\) and \(\overrightarrow{KN}=\begin{pmatrix}-1\\ 4\end{pmatrix}\).
- Find the coordinates of \(L\), \(N\) and \(M\).[3]
- Write down \(\overrightarrow{LM}\) as a column vector.[1]
- Find the length of \(KL\), leaving your answer as a surd.[1]
Solution:
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Answer:(a) \(L(3,\ 4)\), \(N(-3,\ 5)\), \(M(2,\ 8)\) (b) \(\overrightarrow{LM}=\begin{pmatrix}-1\\ 4\end{pmatrix}\) (c) \(\sqrt{34}\) units
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