The sentence needs to be in passive voice because of "by the rapid motion". Hence B, D and E are out. Between A and C what's the difference between "to which" and "that" and more important their usage
1. In astronomy the term “red shift” denotes the extent to which light from a distant galaxy has been shifted toward the red, or long-wave, end of the light spectrum by the rapid motion of the galaxy away from the Earth.
(A) to which light from a distant galaxy has been shifted
(B) to which light from a distant galaxy has shifted
(C) that light from a distant galaxy has been shifted
(D) of light from a distant galaxy shifting
(E) of the shift of light from a distant galaxy
Spoiler Official Answer is A
Change A in this way:
light from a distant galaxy has been shifted to the extend ...
I think this is a very useful way to examine prepositions (to) before Relative pronouns (which)
Another way to reinforce that A is correct is to make up a question for which this sentence (or a portion of it, in this case) would be the answer. If you do this, a properly structured question would be...
"To what extent is light from a distant galaxy shifted toward the red end of the light sprectrum by the rapid motion of the galaxy away from the earth?"
At least to me, it seems more obvious that the "to" needs to come along with the "extent" when you word is at a question.
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