| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2023 |
| Session | September |
| Marks | 6 |
| Topic | Straight Lines & Coordinate Geometry |
| Type | Coordinates from geometric constraints |
| Difficulty | Moderate -0.8 This is a straightforward coordinate geometry question requiring only standard techniques: midpoint formula to find C's coordinates (part a), then finding a perpendicular line and its intersection with a horizontal line (part b). All steps are routine A-level procedures with no problem-solving insight needed, making it easier than average but not trivial due to the multi-step nature. |
| Spec | 1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.03b Straight lines: parallel and perpendicular relationships |
\includegraphics{figure_2}
The figure above shows a triangle with vertices at $A(2,6)$, $B(11,6)$ and $C(p,q)$.
\begin{enumerate}[label=(\alph*)]
\item Given that the point $D(6,2)$ is the midpoint of $AC$, determine the value of $p$ and the value of $q$. [2]
\end{enumerate}
The straight line $l$ passes through $D$ and is perpendicular to $AC$.
The point $E$ is the intersection of $l$ and $AB$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the coordinates of $E$. [4]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Pure 2023 Q2 [6]}}