1 The triangle \(A B C\) has vertices \(A ( - 2,3 ) , B ( 4,1 )\) and \(C ( 2 , - 5 )\).
- Find the coordinates of the mid-point of \(B C\).
- Find the gradient of \(A B\), in its simplest form.
- Hence find an equation of the line \(A B\), giving your answer in the form \(x + q y = r\), where \(q\) and \(r\) are integers.
- Find an equation of the line passing through \(C\) which is parallel to \(A B\).
- Prove that angle \(A B C\) is a right angle.