<p>\(A\) is the point \((4,-2)\) and the line \(AB\) is parallel to the line \(\frac{1}{2}x-3y=9\).</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Find the equation of the line \(AB\).<span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">The equation of the line \(BC\) is \(2x+9y+52=0\).<br>Find the \(x\)-coordinate of \(B\).<br><span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">It is given that&nbsp;\(\overrightarrow{AD}=\begin{pmatrix} 3\\3 \end{pmatrix}\) and \(\overrightarrow{AE}=\begin{pmatrix} 5 \\ 1 \end{pmatrix}\).</div><ol class="i-list"><li><div class="list-item-paragraph">By considering their magintudes, show that&nbsp;\(ADE\) is a right-angled triangle.<span class="inline-marks">[3]</span></div></li><li><div class="list-item-paragraph">\(F\) is the point \((0,-6)\). Showing your working, determine if&nbsp;\(F\) lies on \(DA\) extended.<span class="inline-marks">[2]</span></div></li></ol></li></ol>

\(A\) is the point \((4,-2)\) and the line \(AB\) is parallel to the line \(\frac{1}{2}x-3y=9\).

The equation of the line \(BC\) is \(2x+9y+52=0\).
Find the \(x\)-coordinate of \(B\).


It is given that \(\overrightarrow{AD}=\begin{pmatrix} 3\\3 \end{pmatrix}\) and \(\overrightarrow{AE}=\begin{pmatrix} 5 \\ 1 \end{pmatrix}\).

Vectors

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