9 The points \(A , B\) and \(C\) have coordinates \(( 5,1 ) , ( p , 7 )\) and \(( 8,2 )\) respectively.
- Given that the distance between points \(A\) and \(B\) is twice the distance between points \(A\) and \(C\), calculate the possible values of \(p\).
- Given also that the line passing through \(A\) and \(B\) has equation \(y = 3 x - 14\), find the coordinates of the mid-point of \(A B\).