Edexcel C1 — Question 8 9 marks

Exam BoardEdexcel
ModuleC1 (Core Mathematics 1)
Marks9
PaperDownload PDF ↗
TopicStraight Lines & Coordinate Geometry
TypeCoordinates from geometric constraints
DifficultyModerate -0.8 This is a straightforward coordinate geometry question requiring only standard techniques: midpoint formula (part a), perpendicular gradient and line equation (part b), and solving simultaneous equations (part c). All methods are routine C1 content with no problem-solving insight needed, making it easier than average but not trivial due to the multi-step nature.
Spec1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.03b Straight lines: parallel and perpendicular relationships

\includegraphics{figure_2} The points \(A(1, 7)\), \(B(20, 7)\) and \(C(p, q)\) form the vertices of a triangle \(ABC\), as shown in Figure 2. The point \(D(8, 2)\) is the mid-point of \(AC\).
  1. Find the value of \(p\) and the value of \(q\). [2]
The line \(l\), which passes through \(D\) and is perpendicular to \(AC\), intersects \(AB\) at \(E\).
  1. Find an equation for \(l\), in the form \(ax + by + c = 0\), where \(a\), \(b\) and \(c\) are integers. [5]
  2. Find the exact \(x\)-coordinate of \(E\). [2]

\includegraphics{figure_2}

The points $A(1, 7)$, $B(20, 7)$ and $C(p, q)$ form the vertices of a triangle $ABC$, as shown in Figure 2. The point $D(8, 2)$ is the mid-point of $AC$.

\begin{enumerate}[label=(\alph*)]
\item Find the value of $p$ and the value of $q$. [2]
\end{enumerate}

The line $l$, which passes through $D$ and is perpendicular to $AC$, intersects $AB$ at $E$.

\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find an equation for $l$, in the form $ax + by + c = 0$, where $a$, $b$ and $c$ are integers. [5]
\item Find the exact $x$-coordinate of $E$. [2]
\end{enumerate}

\hfill \mbox{\textit{Edexcel C1  Q8 [9]}}