<-y,x> has a magnitude of: $y ^{2}+x ^{2}.$ And that magnitude is an equation for a circle. So we can represent that magnitude by $r ^{2}.$ In order to scale that magnitude to the required magnitude of:$\frac{ 1 }{ r },$ we need to multiply the vector <-y,x> by $\frac{ 1 }{ r ^{2} }.$