8. The points \(A ( - 1 , - 2 ) , B ( 7,2 )\) and \(C ( k , 4 )\), where \(k\) is a constant, are the vertices of \(\triangle A B C\). Angle \(A B C\) is a right angle.
- Find the gradient of \(A B\).
- Calculate the value of \(k\).
- Show that the length of \(A B\) may be written in the form \(p \sqrt { 5 }\), where \(p\) is an integer to be found.
- Find the exact value of the area of \(\triangle A B C\).
- Find an equation for the straight line \(l\) passing through \(B\) and \(C\). Give your answer in the form \(a x + b y + c = 0\), where \(a , b\) and \(c\) are integers.