| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2007 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | 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 routine techniques: rearranging to find gradient, solving simultaneous equations for intersection, and calculating triangle area using standard methods. All steps are mechanical with no problem-solving insight needed, making it easier than average but not trivial since it requires multiple coordinated steps. |
| Spec | 1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.03b Straight lines: parallel and perpendicular relationships |
\begin{enumerate}
\item The line $l _ { 1 }$ has equation $y = 3 x + 2$ and the line $l _ { 2 }$ has equation $3 x + 2 y - 8 = 0$.\\
(a) Find the gradient of the line $l _ { 2 }$.
\end{enumerate}
The point of intersection of $l _ { 1 }$ and $l _ { 2 }$ is $P$.\\
(b) Find the coordinates of $P$.
The lines $l _ { 1 }$ and $l _ { 2 }$ cross the line $y = 1$ at the points $A$ and $B$ respectively.\\
(c) Find the area of triangle $A B P$.\\
\hfill \mbox{\textit{Edexcel C1 2007 Q11 [9]}}