| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2012 |
| Session | June |
| Marks | 15 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Straight Lines & Coordinate Geometry |
| Type | Perpendicular line through point |
| Difficulty | Standard +0.3 This is a multi-part coordinate geometry question covering standard C1 topics: finding points on lines, perpendicular gradients, intersections, and distance calculations. Parts (a)-(d) are routine applications of formulas. Part (e) requires more steps (finding multiple points, calculating area) but uses only standard techniques with no novel insight needed. Slightly easier than average due to straightforward methodology throughout. |
| Spec | 1.02q Use intersection points: of graphs to solve equations1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.03b Straight lines: parallel and perpendicular relationships |
9. The line $L _ { 1 }$ has equation $4 y + 3 = 2 x$
The point $A ( p , 4 )$ lies on $L _ { 1 }$
\begin{enumerate}[label=(\alph*)]
\item Find the value of the constant $p$.
The line $L _ { 2 }$ passes through the point $C ( 2,4 )$ and is perpendicular to $L _ { 1 }$
\item Find an equation for $L _ { 2 }$ giving your answer in the form $a x + b y + c = 0$, where $a , b$ and $c$ are integers.
The line $L _ { 1 }$ and the line $L _ { 2 }$ intersect at the point $D$.
\item Find the coordinates of the point $D$.
\item Show that the length of $C D$ is $\frac { 3 } { 2 } \sqrt { } 5$
A point $B$ lies on $L _ { 1 }$ and the length of $A B = \sqrt { } ( 80 )$\\
The point $E$ lies on $L _ { 2 }$ such that the length of the line $C D E = 3$ times the length of $C D$.
\item Find the area of the quadrilateral $A C B E$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 2012 Q9 [15]}}