She traced her family history … matrilineal.

Analyze the question The sentence is "She traced her family history _ matrilineal." We need the preposition that correctly links "traced her family history" to "matrilineal" (descent through the mother's line).

Explain the concept "Matrilineal" is an adjective meaning descent through the female or maternal line. The word "line" gives a clue. A preposition is needed that shows the method or means of tracing, and "by" is used for this. Examples:

• "He traced his ancestry by the paternal line."
• "Descent is reckoned by the mother's side."

However, "in the matrilineal line" is also a common idiom ("descent in the female line"). So we need to check each option carefully.

Test the options

• A. At: "traced at matrilineal" does not make sense. "At" is used for points in time or place.
• B. In: "traced her family history in matrilineal" is awkward because "in" needs a noun such as "line" after it (e.g., "in the matrilineal line"). It does not work directly before the adjective.
• C. By: "traced her family history by matrilineal" shows the method or route of tracing.
• D. With: "with" suggests accompaniment or instrument, so it does not fit here.

Answer The best choice is C. By. The sentence reads: She traced her family history by matrilineal (descent).

Tip: When a gap shows the method or way something is done (trace by, reckon by, judge by), think "by". Also remember "in" usually needs a full noun phrase after it, while "by" can work more flexibly here.