Edexcel C12 2017 October — Question 10

Exam BoardEdexcel
ModuleC12 (Core Mathematics 1 & 2)
Year2017
SessionOctober
TopicStraight Lines & Coordinate Geometry

10. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{bb1becd5-96c1-426d-9b85-4bbc4a61af27-24_863_929_255_511} \captionsetup{labelformat=empty} \caption{Figure 4}
\end{figure} Diagram NOT drawn to scale The points \(A ( 7 , - 3 ) , B ( 7,20 )\) and \(C ( p , q )\) form the vertices of a triangle \(A B C\), as shown in Figure 4. The point \(D ( 10,5 )\) is the midpoint of \(A C\).
  1. Find the value of \(p\) and the value of \(q\). The line \(l\) passes through \(D\) and is perpendicular to \(A C\).
  2. Find an equation for \(l\), in the form \(a x + b y = c\), where \(a\), \(b\) and \(c\) are integers. Given that the line \(l\) intersects \(A B\) at \(E\),
  3. find the exact coordinates of \(E\).