Question

suppose the parallelogram on the coordinate plane was dilated with respect to the origin using a magnitude of 1/2 what wold be the coordinates of vertex D' (2,-2)

Answer 1

Dilation about the origin by factor 1/2 multiplies each coordinate by 1/2. So if the original vertex D is (2, −2), the image D' is

D' = (2·1/2, −2·1/2) = (1, −1).

(If instead (2, −2) were already D', the preimage would be (4, −4).)