Question 418035
The possible coordinates of R(x,y) are on the circle of radius {{{ 4*sqrt(2)}}} and center point Q(3,4). The equation of the circle is: {{{(x-3)^2+(y-4)^2=32 }}}
The equation of line PQ is; y=-x+7 and the equation of line QR perpendicular to PQ
is: y=x+1. The possible coordinates of R(x,y) are on intersection of the line QR with circle. If we solve the system which contains these two equations: {{{ y=x+1 and (x-3)^2+(y-4)^2=32}}}, we find coordinates of two points which are: 
  R[3+4*sqrt(2), 4+4*sqrt(2)] ,  R'[3-4*sqrt(2), 4-4*sqrt(2)]