I think you forget to type the vertices of dot D. We suppose D is (2a, x). Then we can get the length of CD is [tex] \sqrt{(2a-a)^{2}+ (x-b)^{2} } [/tex]. So the length of C^1D^1 after dilation with scale factor of 2, it is 2[tex] \sqrt{a^{2}+ (x-b)^{2} } [/tex].