| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2009 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Topic | Straight Lines & Coordinate Geometry |
| Type | Perpendicular from point to line |
| Difficulty | Moderate -0.3 This is a structured multi-part question covering standard coordinate geometry techniques (perpendicular gradients, simultaneous equations, distance formula, triangle area). While it requires multiple steps across 5 parts, each individual technique is routine for C1 level with clear scaffolding. The final parts connect concepts but don't require novel insight—slightly easier than average due to the guided structure. |
| Spec | 1.02c Simultaneous equations: two variables by elimination and substitution1.03b Straight lines: parallel and perpendicular relationships |
\includegraphics{figure_11}
Fig. 11 shows the line joining the points A $(0, 3)$ and B $(6, 1)$.
\begin{enumerate}[label=(\roman*)]
\item Find the equation of the line perpendicular to AB that passes through the origin, O. [2]
\item Find the coordinates of the point where this perpendicular meets AB. [4]
\item Show that the perpendicular distance of AB from the origin is $\frac{9\sqrt{10}}{10}$. [2]
\item Find the length of AB, expressing your answer in the form $a\sqrt{10}$. [2]
\item Find the area of triangle OAB. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C1 2009 Q11 [12]}}