Question

Find the coordinates of the image of the point p(4,6)under the reflection about the line x=3 followed by the reflection about the line y=x.

Answer 1

reflect through x=3: (x,y)->(3-(x-3),y) = (6-x,y)

reflect through y=x: (x,y)->(y,x)

so, now just combine those two transformations:

(x,y)->(6-x,y)->(y,6-x)