The answer
\(BC = \sqrt{117} \approx 10.8\)
O-Level E-Math 2017 Paper 1 Question 12 · Verified worked solution by the Genius Plus Academy teaching team
The question
\(ABC\) is a triangle with \(\overrightarrow{AB} = \begin{pmatrix} 5 \\ -1 \end{pmatrix}\) and \(\overrightarrow{AC} = \begin{pmatrix} -1 \\ 8 \end{pmatrix}\). Calculate the length of \(BC\). [3]
\(\overrightarrow{BC} = \overrightarrow{AC} - \overrightarrow{AB} = \begin{pmatrix} -1 \\ 8 \end{pmatrix} - \begin{pmatrix} 5 \\ -1 \end{pmatrix} = \begin{pmatrix} -6 \\ 9 \end{pmatrix}\). Then \[|BC| = \sqrt{(-6)^2 + 9^2} = \sqrt{36 + 81} = \sqrt{117} = 10.8 \text{ (3 s.f.)}.\]
Answer: \(BC = \sqrt{117} \approx 10.8\)
Same structure, different numbers
Swap the constants, dress a quadratic as a length, hide a derivative inside an integral, and a student sees a brand new problem. The structure underneath is the same, and so is the method. Once a student can name the structure, a whole row of questions that look different start to open the same way.
That is where marks really leak: in choosing the method, not in the algebra that follows. We call it Lock and Key, name the lock, then the key follows.
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Genius Plus Academy · O-Level & IP Mathematics
Our O-Level E-Math tuition trains the same recognise-the-structure method these worked solutions show, taught by a team that has marked these papers for years. It runs within our weekly Secondary Math programme, Sec 1 to 4 and IP.
It is a difference of two vectors question from Vectors in two dimensions, worth 3 marks.
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