Concept:The question tests the correct preposition that shows the method or means of tracing a family line.
Explanation:The sentence requires a word that links the action of tracing to the idea of the maternal line.
"By" is the preposition used to express the method, manner, or means of doing something.
It appears in common phrases like "by inheritance," "by blood," or "by tradition."
When tracing is done along the mother's line, the appropriate expression is "by matrilineal."
"At" and "in" are prepositions of place or time, so they do not indicate a method.
"With" would suggest using a tool or being accompanied, which does not fit the meaning.
Thus, the gap is best filled with "by."
The complete sentence becomes: "She traced her family history by matrilineal."
Answer:C. By