5 A line has gradient - 4 and passes through the point (2,6). Find the coordinates of its points of intersection with the axes.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{01569a16-66ba-422e-a74d-6f9430dd245b-3_433_835_353_715}
\captionsetup{labelformat=empty}
\caption{Fig. 11}
\end{figure}
Fig. 11 shows the line joining the points \(\mathrm { A } ( 0,3 )\) and \(\mathrm { B } ( 6,1 )\).
- Find the equation of the line perpendicular to AB that passes through the origin, O .
- Find the coordinates of the point where this perpendicular meets AB .
- Show that the perpendicular distance of AB from the origin is \(\frac { 9 \sqrt { 10 } } { 10 }\).
- Find the length of AB , expressing your answer in the form \(a \sqrt { 10 }\).
- Find the area of triangle OAB .