| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2014 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Straight Lines & Coordinate Geometry |
| Type | Perpendicular line through point |
| Difficulty | Moderate -0.3 This is a standard C1 coordinate geometry question requiring finding a perpendicular line equation (using negative reciprocal of gradient), finding intersection points, and calculating triangle area. All techniques are routine and well-practiced, though the multi-step nature and area calculation requiring exact fractional form adds slight complexity beyond the most basic exercises. |
| Spec | 1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.03b Straight lines: parallel and perpendicular relationships |
| Answer | Marks |
|---|---|
| (a) \(2x + 3y = 26 \Rightarrow 3y = 26 \pm 2x\) and attempt to find \(m\) from \(y = mx + c\) | M1 |
| \((\Rightarrow y = \frac{26}{3} - \frac{2}{3}x)\) so gradient \(= -\frac{2}{3}\) | A1 |
| Gradient of perpendicular \(= \frac{-1}{\text{their gradient}} (-\frac{3}{2})\) | M1 |
| Line goes through \((0,0)\) so \(y = \frac{3}{2}x\) | A1 |
| **(4 marks |
**(a)** $2x + 3y = 26 \Rightarrow 3y = 26 \pm 2x$ and attempt to find $m$ from $y = mx + c$ | M1 |
$(\Rightarrow y = \frac{26}{3} - \frac{2}{3}x)$ so gradient $= -\frac{2}{3}$ | A1 |
Gradient of perpendicular $= \frac{-1}{\text{their gradient}} (-\frac{3}{2})$ | M1 |
Line goes through $(0,0)$ so $y = \frac{3}{2}x$ | A1 |
| | **(4 marks9.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{64f015bf-29fb-4374-af34-3745ea49aced-12_675_863_267_552}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{center}
\end{figure}
The line $l _ { 1 }$, shown in Figure 2 has equation $2 x + 3 y = 26$\\
The line $l _ { 2 }$ passes through the origin $O$ and is perpendicular to $l _ { 1 }$
\begin{enumerate}[label=(\alph*)]
\item Find an equation for the line $l _ { 2 }$
The line $l _ { 2 }$ intersects the line $l _ { 1 }$ at the point $C$.\\
Line $l _ { 1 }$ crosses the $y$-axis at the point $B$ as shown in Figure 2.
\item Find the area of triangle $O B C$.
Give your answer in the form $\frac { a } { b }$, where $a$ and $b$ are integers to be determined.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 2014 Q9 [10]}}