| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Straight Lines & Coordinate Geometry |
| Type | Intersection of two lines |
| Difficulty | Moderate -0.8 This is a straightforward multi-part coordinate geometry question requiring standard techniques: point-slope form to equation of line, simultaneous equations to find intersection, and triangle area formula. All methods are routine C1 procedures with no problem-solving insight needed, making it easier than average but not trivial due to the multi-step nature and 10 total marks. |
| Spec | 1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.03b Straight lines: parallel and perpendicular relationships |
The line $l_1$ passes through the point $(9, -4)$ and has gradient $\frac{1}{3}$.
\begin{enumerate}[label=(\alph*)]
\item Find an equation for $l_1$ in the form $ax + by + c = 0$, where $a$, $b$ and $c$ are integers. [3]
\end{enumerate}
The line $l_2$ passes through the origin $O$ and has gradient $-2$. The lines $l_1$ and $l_2$ intersect at the point $P$.
\begin{enumerate}[label=(\alph*)]
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\item Calculate the coordinates of $P$. [4]
\end{enumerate}
Given that $l_1$ crosses the $y$-axis at the point $C$,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item calculate the exact area of $\triangle OCP$. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q8 [10]}}