OCR MEI C1 2009 June — Question 11

Exam BoardOCR MEI
ModuleC1 (Core Mathematics 1)
Year2009
SessionJune
TopicStraight Lines & Coordinate Geometry

11 \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{1209192c-655e-439d-be50-8747dbbb7672-3_444_846_351_648} \captionsetup{labelformat=empty} \caption{Fig. 11}
\end{figure} Fig. 11 shows the line joining the points \(\mathrm { A } ( 0,3 )\) and \(\mathrm { B } ( 6,1 )\).
  1. Find the equation of the line perpendicular to AB that passes through the origin, O .
  2. Find the coordinates of the point where this perpendicular meets AB .
  3. Show that the perpendicular distance of AB from the origin is \(\frac { 9 \sqrt { 10 } } { 10 }\).
  4. Find the length of AB , expressing your answer in the form \(a \sqrt { 10 }\).
  5. Find the area of triangle OAB .