| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 9 |
| 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: sketching lines (finding intercepts), solving simultaneous equations, and finding a perpendicular line equation. All methods are routine with no problem-solving insight needed, making it easier than average, though the multi-part structure and exact fraction requirement prevent it from being trivial. |
| 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 relationships |
The straight line $l_1$ has equation $4y + x = 0$.
The straight line $l_2$ has equation $y = 2x - 3$.
\begin{enumerate}[label=(\alph*)]
\item On the same axes, sketch the graphs of $l_1$ and $l_2$. Show clearly the coordinates of all points at which the graphs meet the coordinate axes. [3]
\end{enumerate}
The lines $l_1$ and $l_2$ intersect at the point $A$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Calculate, as exact fractions, the coordinates of $A$. [3]
\item Find an equation of the line through $A$ which is perpendicular to $l_1$. Give your answer in the form $ax + by + c = 0$, where $a$, $b$ and $c$ are integers. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q10 [9]}}