<p><strong>Solutions to this question by accurate drawing will not be accepted.</strong></p>
<p>The diagram shows a right-angled triangle \(ABC\) where&nbsp;\(\angle ABC = 90^\circ\). The coordinates of \(A\) and \(B\) are \((-8, -4)\) and \((4, 14)\) respectively.</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="i-list"><li><div class="list-item-paragraph">Find the equation of the line \(BC\).</div></li><li><div class="list-item-paragraph">Find the coordinates of \(P\) and of \(Q\), where&nbsp;\(P\) lies on the \(y\)-axis and \(Q\) is the intersection of line \(BC\) and the \(x\)-axis.</div></li><li><div class="list-item-paragraph">Given that&nbsp;\(BC = 2AB\), find the coordinates of \(C\).</div></li><li><div class="list-item-paragraph">Find the area of the quadrilateral \(APQC\).</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1772355466409-wnfvu9k43ho.png" style="max-width: min(300px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div></div></div></div>

**Solutions to this question by accurate drawing will not be accepted.**

The diagram shows a right-angled triangle \(ABC\) where \(\angle ABC = 90^\circ\). The coordinates of \(A\) and \(B\) are \((-8, -4)\) and \((4, 14)\) respectively.

Coordinate Geometry

Coordinate Geometry