The correct answer is A. Sentence A uses the pronoun "me" in the objective case.
All of the sentences, along with an explanation, are below:
Father took ~ME~ on a plane ride to take aerial photos for mapmaking.
-- Here, "me" is in the objective case because it is the object of the verb "took." Once we identify the verb (took), we can identify the subject by asking "who or what took?" That tells us the subject: Father. Father took what? The answer to that question is the object: Me. Therefore, the pronoun "me" is the object of the sentence, making it in the objective case.
~THEY~ went with Father on a plane ride to take aerial photos for mapmaking.
-- Here, "they" is the subject of the sentence. We can tell this by identifying the verb: went. Who or what went? They went. Therefore, the pronoun "they" is the subject of the sentence, making it in the subjective case.
~MY~ trip with Father, on a plane ride to take aerial photos for mapmaking, was exciting.
-- Here, "my" is being used to describe the trip. Whose trip? MY trip. Therefore, this pronoun is adjectival in nature.
~I~ went with Father on a plane ride to take aerial photos for mapmaking.
-- Here, "I" is the subject of the sentence. We can tell this by identifying the verb: went. Who or what went? I went. Therefore, the pronoun "I" is the subject of the sentence, making it in the subjective case.
