| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Straight Lines & Coordinate Geometry |
| Type | Rectangle or parallelogram vertices |
| Difficulty | Moderate -0.8 This is a straightforward C1 coordinate geometry question involving basic gradient calculations (perpendicular lines have negative reciprocal gradients), distance formula application, and solving a simple equation. All techniques are standard and the multi-step nature is scaffolded with clear parts, making it easier than average for A-level. |
| Spec | 1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.03b Straight lines: parallel and perpendicular relationships1.10f Distance between points: using position 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 Q3 [11]}}