<p>In the diagram, \(C\) is the point \((0,15)\) and \(B\) is the point \((0,5)\).</p>
<p>The sloping line through \(C\) and the horizontal line through \(B\) meet at point \(A\).</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Write down the equation of the line \(AB\).</span></div></li><li><div class="list-item-content"><span class="list-item-text">Given that the gradient of the line \(AC\) is \(2\), find the equation of the line \(AC\).</span></div></li><li><div class="list-item-content"><span class="list-item-text">Calculate the coordinates of the point \(A\).</span></div></li></ol>
<div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1772349748320-e8rjqmjxkyr.png" style="max-width: min(300px, 100%); height: auto; display: block;" alt="Coordinate geometry diagram showing points A, B, and C on a Cartesian plane." class="alignright custom-width" /></figure></div>

In the diagram, \(C\) is the point \((0,15)\) and \(B\) is the point \((0,5)\).

The sloping line through \(C\) and the horizontal line through \(B\) meet at point \(A\).

Write down the equation of the line \(AB\).

Given that the gradient of the line \(AC\) is \(2\), find the equation of the line \(AC\).

Calculate the coordinates of the point \(A\).

Coordinate Geometry

Question 77e854f9