find the direction vector from (3,2) to (7,1) ...

direction vector is (7-3,1-2) = (4,-1)

note the slope of the direction vector ... -1/4

a perpendicular slope would be +4/1, so the perpendicular direction vector is (1,4)

translate the perpendicular direction vector so that its tail is at (3,2) ...

(1+3, 4+2) = (4,6), the image coordinates.

I'll leave it for you to find the image for the general rotation.