1 The point \(A\) has coordinates (6, -4) and the point \(B\) has coordinates (-2, 7).
- Given that the point \(O\) has coordinates \(( 0,0 )\), show that the length of \(O A\) is less than the length of \(O B\).
- Find the gradient of \(A B\).
- Find an equation of the line \(A B\) in the form \(p x + q y = r\), where \(p , q\) and \(r\) are integers.
- The point \(C\) has coordinates \(( k , 0 )\). The line \(A C\) is perpendicular to the line \(A B\). Find the value of the constant \(k\).