Standard +0.3 This is a coordinate geometry problem requiring calculation of gradients, perpendicular/parallel line conditions, and solving simultaneous equations. While it involves multiple steps (finding gradient of AB, using perpendicular condition for DA, using parallel condition for DC, finding intersection), these are all standard techniques taught early in P1. The problem is slightly above average difficulty due to the need to coordinate multiple conditions, but remains a straightforward application of core principles without requiring novel insight.
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\includegraphics[max width=\textwidth, alt={}, center]{e753f588-97bc-4c6a-a82b-7b6a6d0cadc4-2_627_748_1685_699}
The three points \(A ( 3,8 ) , B ( 6,2 )\) and \(C ( 10,2 )\) are shown in the diagram. The point \(D\) is such that the line \(D A\) is perpendicular to \(A B\) and \(D C\) is parallel to \(A B\). Calculate the coordinates of \(D\).
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\includegraphics[max width=\textwidth, alt={}, center]{e753f588-97bc-4c6a-a82b-7b6a6d0cadc4-2_627_748_1685_699}
The three points $A ( 3,8 ) , B ( 6,2 )$ and $C ( 10,2 )$ are shown in the diagram. The point $D$ is such that the line $D A$ is perpendicular to $A B$ and $D C$ is parallel to $A B$. Calculate the coordinates of $D$.
\hfill \mbox{\textit{CAIE P1 2007 Q6 [7]}}