1 The points \(A\) and \(B\) have coordinates \(( 1,6 )\) and \(( 5 , - 2 )\) respectively. The mid-point of \(A B\) is \(M\).
- Find the coordinates of \(M\).
- Find the gradient of \(A B\), giving your answer in its simplest form.
- A straight line passes through \(M\) and is perpendicular to \(A B\).
- Show that this line has equation \(x - 2 y + 1 = 0\).
- Given that this line passes through the point \(( k , k + 5 )\), find the value of the constant \(k\).