| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Straight Lines & Coordinate Geometry |
| Type | Rectangle or parallelogram vertices |
| Difficulty | Moderate -0.8 This is a straightforward coordinate geometry question requiring basic gradient calculations, Pythagoras' theorem, and understanding of rectangle properties. All steps are routine: finding perpendicular gradients, using distance formula, solving a simple quadratic, and applying vector addition. No novel insight required, just methodical application of standard techniques. |
| Spec | 1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.03b Straight lines: parallel and perpendicular relationships1.03c Straight line models: in variety of contexts1.03d Circles: equation (x-a)^2+(y-b)^2=r^21.03e Complete the square: find centre and radius of circle |
3.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{90893903-4f36-4974-8eaa-0f462f35f442-02_650_1043_367_317}
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\caption{Fig. 2}
\end{center}
\end{figure}
The points $A ( 3,0 )$ and $B ( 0,4 )$ are two vertices of the rectangle $A B C D$, as shown in Fig. 2.
\begin{enumerate}[label=(\alph*)]
\item Write down the gradient of $A B$ and hence the gradient of $B C$.
The point $C$ has coordinates $( 8 , k )$, where $k$ is a positive constant.
\item Find the length of $B C$ in terms of $k$.
Given that the length of $B C$ is 10 and using your answer to part (b),
\item find the value of $k$,
\item find the coordinates of $D$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 Q3 [11]}}