Find the gradient of the line \(l _ { 1 }\) which has equation \(4 x - 3 y + 5 = 0\).
Find an equation of the line \(l _ { 2 }\), which passes through the point ( 1,2 ) and which is perpendicular to the line \(l _ { 1 }\), giving your answer in the form \(a x + b y + c = 0\).
The line \(l _ { 1 }\) crosses the \(x\)-axis at \(P\) and the line \(l _ { 2 }\) crosses the \(y\)-axis at \(Q\).
Find the coordinates of the mid-point of \(P Q\).
Calculate the length of \(P Q\), giving your answer in the form \(\frac { \sqrt { } a } { b }\), where \(a\) and \(b\) are integers.