| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Straight Lines & Coordinate Geometry |
| Type | Coordinates from geometric constraints |
| Difficulty | Moderate -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. |
| Spec | 1.03a 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 $AC$.
\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]}}