| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 11 |
| 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 testing standard techniques: finding a point on the y-axis, midpoint formula, perpendicular gradient, and solving simultaneous equations. All methods are routine C1 procedures with no problem-solving insight required, making it easier than average but not trivial due to the multiple steps involved. |
| Spec | 1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.03b Straight lines: parallel and perpendicular relationships |
The straight line $l_1$ with equation $y = \frac{3}{2}x - 2$ crosses the $y$-axis at the point $P$. The point $Q$ has coordinates $(5, -3)$.
The straight line $l_2$ is perpendicular to $l_1$ and passes through $Q$.
\begin{enumerate}[label=(\alph*)]
\item Calculate the coordinates of the mid-point of $PQ$. [3]
\item Find an equation for $l_2$ in the form $ax + by = c$, where $a$, $b$ and $c$ are integer constants. [4]
\end{enumerate}
The lines $l_1$ and $l_2$ intersect at the point $R$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Calculate the exact coordinates of $R$. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q23 [11]}}