The diagram shows the points \(A(-3,5)\) and \(B(5,-1)\). The midpoint of \(AB\) is \(M\), and the line \(PM\) is perpendicular to \(AB\). The point \(P\) has coordinates \((r,s)\).

(i) Find the equation of the line \(PM\) in the form \(y=mx+c\), where \(m\) and \(c\) are exact constants.

(ii) Hence find an expression for \(s\) in terms of \(r\).

(iii) Given that the length of \(PM\) is \(10\) units, find the value of \(r\) and of \(s\).