| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 15 |
| Paper | Download PDF ↗ |
| Topic | Straight Lines & Coordinate Geometry |
| Type | Intersection of two lines |
| Difficulty | Moderate -0.3 This is a standard C1 coordinate geometry question requiring gradient calculation, perpendicular line equations, simultaneous equations, distance formula, and triangle area. While it has multiple parts (15 marks total), each step follows routine procedures with no novel insight required. It's slightly easier than average due to being entirely procedural, though the multi-step nature and 'exact area' requirement prevent it from being significantly below average. |
| Spec | 1.02c Simultaneous equations: two variables by elimination and substitution1.03a 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 |
The line $l_1$ passes through the points $P(-1, 2)$ and $Q(11, 8)$.
\begin{enumerate}[label=(\alph*)]
\item Find an equation for $l_1$ in the form $y = mx + c$, where $m$ and $c$ are constants. [4]
\end{enumerate}
The line $l_2$ passes through the point $R(10, 0)$ and is perpendicular to $l_1$. The lines $l_1$ and $l_2$ intersect at the point $S$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Calculate the coordinates of $S$. [5]
\item Show that the length of $RS$ is $3\sqrt{5}$. [2]
\item Hence, or otherwise, find the exact area of triangle $PQR$. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q11 [15]}}