A dilation is an isometry.
False
A dilation is an isometry if (r,t) --> (kr,t), where k > 1.
T: x --> u
x = (x,y) = (rcost, rsint)
u = (u,v) = (krcost, krsint) = k(rcost, rsint) = kx
T is an isometry if u/kr = x/r, which is in fact the case here in this question.