| 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 C1 coordinate geometry question requiring standard techniques: finding gradient and equation of a line through two points, writing equation of a line through origin, solving simultaneous equations, and finding a midpoint. All steps are routine 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=0 |
The points $A$ and $B$ have coordinates $(4, 6)$ and $(12, 2)$ respectively.
The straight line $l_1$ passes through $A$ and $B$.
\begin{enumerate}[label=(\alph*)]
\item Find an equation for $l_1$ in the form $ax + by = c$, where $a$, $b$ and $c$ are integers. [4]
\end{enumerate}
The straight line $l_2$ passes through the origin and has gradient $-4$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Write down an equation for $l_2$. [1]
\end{enumerate}
The lines $l_1$ and $l_2$ intercept at the point $C$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Find the exact coordinates of the mid-point of $AC$. [5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q27 [10]}}