Consider the isometry of the coordinate plane that is rotation by 90 degrees counterclockwise about the point (1,2).  We will call this transformation T.
We denote
by L ... the translation of the plane by the vector <-1,-2> ,
by T'... the rotation of the plane by 90 degrees about the origin (0,0), and
by L^-1  ... the translation of the plane by the vector <1,2>.
Then T = L^-1T'L  as a transformation.
So

L[	x	]=[	x-1	]=[	x'	]
	y		y-2		y'
T'[	x'	]=[	-y'	]
	y'		x'
L-1[	-y'	]=[	-y' +1	]=[	-(y-2)+1	]
	x		x' +2		x -1 +2
and thus we have
T[	x	]=[	3-y	]
	y		x+1

 
Here is the visualization of T as a map in Winplot using: (x,y)==>(3-y,x+1)

T: Rotation by 90 degrees about (1,2).

Plane before the Application of  T	Plane after the Application of  T