1 The point \(A\) has coordinates \(( - 1,2 )\) and the point \(B\) has coordinates \(( 3 , - 5 )\).
- Find the gradient of \(A B\).
- Hence find an equation of the line \(A B\), giving your answer in the form \(p x + q y = r\), where \(p , q\) and \(r\) are integers.
- The midpoint of \(A B\) is \(M\).
- Find the coordinates of \(M\).
- Find an equation of the line which passes through \(M\) and which is perpendicular to \(A B\). [3 marks]
- The point \(C\) has coordinates \(( k , 2 k + 3 )\). Given that the distance from \(A\) to \(C\) is \(\sqrt { 13 }\), find the two possible values of the constant \(k\).
[0pt]
[4 marks]