| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Straight Lines & Coordinate Geometry |
| Type | Rectangle or parallelogram vertices |
| Difficulty | Moderate -0.8 This is a straightforward coordinate geometry question requiring basic gradient calculations (perpendicular lines), distance formula application, and solving a simple equation. All techniques are standard C1 material with clear step-by-step structure and no novel problem-solving required, making it easier than average but not trivial due to the multi-part nature. |
| Spec | 1.03b Straight lines: parallel and perpendicular relationships1.10c Magnitude and direction: of vectors |
\includegraphics{figure_2}
The points $A (3, 0)$ and $B (0, 4)$ are two vertices of the rectangle $ABCD$, as shown in Fig. 2.
\begin{enumerate}[label=(\alph*)]
\item Write down the gradient of $AB$ and hence the gradient of $BC$.
[3]
\end{enumerate}
The point $C$ has coordinates $(8, k)$, where $k$ is a positive constant.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the length of $BC$ in terms of $k$.
[2]
\end{enumerate}
Given that the length of $BC$ is 10 and using your answer to part (b),
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item find the value of $k$,
[4]
\item find the coordinates of $D$.
[2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q6 [11]}}