| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2022 |
| Session | June |
| Marks | 5 |
| Topic | Straight Lines & Coordinate Geometry |
| Type | Parallel line through point |
| Difficulty | Moderate -0.8 This is a straightforward coordinate geometry question requiring standard techniques: (i) finding a parallel line through a given point using the same gradient, and (ii) finding a perpendicular line using the negative reciprocal gradient. Both are routine A-level procedures with no problem-solving insight needed, making it easier than average but not trivial due to the algebraic manipulation required. |
| Spec | 1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.03b Straight lines: parallel and perpendicular relationships |
The trapezium $ABCD$ is shown below.
\includegraphics{figure_2}
The line $AB$ has equation $2x + 3y = 14$ and $DC$ is parallel to $AB$.
The point D has coordinates $(3, 7)$.
\begin{enumerate}[label=(\roman*)]
\item Find an equation of the line DC [2 marks]
\item The angle BAD is a right angle. Find an equation of the line AD, giving your answer in the form $mx + ny + p = 0$, where $m$, $n$ and $p$ are integers. [3 marks]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Pure 2022 Q2 [5]}}