Edexcel C1 — Question 10

Exam BoardEdexcel
ModuleC1 (Core Mathematics 1)
TopicStraight Lines & Coordinate Geometry

10. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{50145adb-ef84-47d4-ad27-294c141d3822-3_625_1000_1546_264} \captionsetup{labelformat=empty} \caption{Figure 1}
\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. 1.
  1. 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.
  2. 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),
  3. find the value of \(k\),
  4. find the coordinates of \(D\).