| 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 -0.5 This is a straightforward C1 coordinate geometry question requiring standard techniques: finding gradients using perpendicularity, applying Pythagoras' theorem, and solving a simple quadratic. While multi-part with 11 marks total, each step follows directly from the previous with no novel insight required, making it slightly easier than average. |
| Spec | 1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.03b Straight lines: parallel and perpendicular relationships |
| Answer | Marks |
|---|---|
| \(AB\): \(M = -\frac{4}{3}\); \(BC\): \(M = \frac{3}{4}\) | B1, M1, A1 ft (3) |
| Answer | Marks |
|---|---|
| \(BC = \sqrt{8^2 + (k-4)^2}\) (= \(\sqrt{k^2 - 8k + 80}\)) | M1 A1 (2) |
| Answer | Marks |
|---|---|
| \((k^2 - 8k + 80) = 100\) (their \(BC^2 = 100\)) | M1 |
| Answer | Marks |
|---|---|
| \(k = 10\), \(k = -2\) (rejected) | M1 A1 (4) |
| Answer | Marks |
|---|---|
| \((11, 6)\) | B1 B1 (2) |
## Part (a)
$AB$: $M = -\frac{4}{3}$; $BC$: $M = \frac{3}{4}$ | B1, M1, A1 ft (3)
## Part (b)
$BC = \sqrt{8^2 + (k-4)^2}$ (= $\sqrt{k^2 - 8k + 80}$) | M1 A1 (2)
## Part (c)
$(k^2 - 8k + 80) = 100$ (their $BC^2 = 100$) | M1
$k^2 - 8k - 20 = 0$ → $(k-10)(k+2) = 0$
$k = 10$, $k = -2$ (rejected) | M1 A1 (4)
## Part (d)
$(11, 6)$ | B1 B1 (2)
**Total: 11 marks**\includegraphics{figure_1}
The points $A(3, 0)$ and $B(0, 4)$ are two vertices of the rectangle $ABCD$, as shown in Fig. 1.
\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 Q10 [11]}}