- The line \(l _ { 1 }\) has equation \(x + 3 y - 11 = 0\)
The point \(A\) and the point \(B\) lie on \(l _ { 1 }\)
Given that \(A\) has coordinates ( \(- 1 , p\) ) and \(B\) has coordinates ( \(q , 2\) ), where \(p\) and \(q\) are integers,
- find the value of \(p\) and the value of \(q\),
- find the length of \(A B\), giving your answer as a simplified surd.
The line \(l _ { 2 }\) is perpendicular to \(l _ { 1 }\) and passes through the midpoint of \(A B\).
- Find an equation for \(l _ { 2 }\) giving your answer in the form \(y = m x + c\), where \(m\) and \(c\) are constants to be found.