Name _______________________________________________
(a) Write the equations for the transformation which consists of a
rotation about the origin of 90o followed by a reflection
about the line y = x.
(b) Write the equations for the inverse of
this transformation.
Solution:
(a) The rotation about the origin by 90o
is given by (x,y) -->(x',y'), where x' = -y and y' = x since Cos
90o = 0 and Sin 90o = 1. Reflection about y=x
is given by (x',y')-->(x", y"), where x" = y' and
y" = x'. So, the equations for the transformation
(x,y)-->(x",y") are x" = x and y" = -y.
(b)
The inverse of this reflection (which is itself) sends
(x",y")-->(x,y) and so has equations given by x = x"
and y = -y". Written as (x,y)-->(x''', y''') we would have
x''' = x and y''' = -y.