10
\includegraphics[max width=\textwidth, alt={}, center]{0e4a249a-9e6a-49d4-996c-fe07b7730f59-16_318_1006_260_568}
Relative to an origin \(O\), the position vectors of the points \(A , B , C\) and \(D\), shown in the diagram, are given by
$$\overrightarrow { O A } = \left( \begin{array} { r }
- 1
3
- 4
\end{array} \right) , \quad \overrightarrow { O B } = \left( \begin{array} { r }
2
- 3
5
\end{array} \right) , \quad \overrightarrow { O C } = \left( \begin{array} { r }
4
- 2
5
\end{array} \right) \quad \text { and } \quad \overrightarrow { O D } = \left( \begin{array} { r }
2
2
- 1
\end{array} \right) .$$
- Show that \(A B\) is perpendicular to \(B C\).
- Show that \(A B C D\) is a trapezium.
- Find the area of \(A B C D\), giving your answer correct to 2 decimal places.