Which word correctly completes the sentence: Sarina is only my half-sister because we have ____________ mothers.

The correct choice is "different," which accurately conveys the relationship between Sarina and the speaker. In the context of half-siblings, it is common for individuals to share one biological parent while having different ones. Thus, using "different" signifies that they do not share the same mother, aligning perfectly with the meaning intended in the sentence.

The other options do not suit the context. "Similar" suggests a likeness, which contradicts the notion of having different mothers. "Opposite" implies a stark contrast that is unrelated to familial relationships and is therefore irrelevant here. "Varying" carries a connotation of change or difference but lacks the specific clarity needed in this familial context. Thus, "different" stands out as the most appropriate choice for conveying the nature of their sibling relationship.