OCR MEI C1 2012 June — Question 10 11 marks

Exam BoardOCR MEI
ModuleC1 (Core Mathematics 1)
Year2012
SessionJune
Marks11
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicStraight Lines & Coordinate Geometry
TypeVerify shape type from coordinates
DifficultyModerate -0.3 This is a straightforward coordinate geometry question requiring standard techniques: distance formula for equal sides, gradient multiplication for perpendicularity, and midpoint formula. All methods are routine C1 content with clear signposting across three parts totaling 11 marks. The multi-part structure and verification aspects make it slightly more substantial than a minimal exercise, but no problem-solving insight is needed—just systematic application of formulas.
Spec1.03b Straight lines: parallel and perpendicular relationships1.10f Distance between points: using position vectors1.10g Problem solving with vectors: in geometry

\includegraphics{figure_10} Fig. 10 is a sketch of quadrilateral ABCD with vertices A \((1, 5)\), B \((-1, 1)\), C \((3, -1)\) and D \((11, 5)\).
  1. Show that \(AB = BC\). [3]
  2. Show that the diagonals AC and BD are perpendicular. [3]
  3. Find the midpoint of AC. Show that BD bisects AC but AC does not bisect BD. [5]

\includegraphics{figure_10}

Fig. 10 is a sketch of quadrilateral ABCD with vertices A $(1, 5)$, B $(-1, 1)$, C $(3, -1)$ and D $(11, 5)$.

\begin{enumerate}[label=(\roman*)]
\item Show that $AB = BC$. [3]
\item Show that the diagonals AC and BD are perpendicular. [3]
\item Find the midpoint of AC. Show that BD bisects AC but AC does not bisect BD. [5]
\end{enumerate}

\hfill \mbox{\textit{OCR MEI C1 2012 Q10 [11]}}