This is ______ boy whom I saw yesterday.

Concept

English uses the definite article "the" before a noun the listener can already identify as a specific one. A defining (restrictive) relative clause often supplies that identification, and the presentational frame "This is ..." points to a specific person who is present — together they make "the" the natural, expected choice. The indefinite articles "a"/"an" instead present a noun as newly introduced and non-specific ("a" before a consonant sound, "an" before a vowel sound). A restrictive clause CAN attach to an indefinite noun in other contexts, but here the identifying "This is ... whom I saw yesterday" frame selects the definite article as the best answer.

Application

1. The blank modifies the noun "boy", which is followed by the clause "whom I saw yesterday" inside the presentational frame "This is ...".

2. "whom I saw yesterday", combined with the pointing frame "This is ...", presents one particular boy the speaker is identifying, so the definite article is the expected fit.

3. An identified, specific noun in this frame takes "the": "This is the boy whom I saw yesterday."

Cross-check

Read each filler in this identifying frame: "This is a boy whom I saw yesterday" re-casts him as someone newly introduced and is not what "This is ..." intends here, "an boy" is not even phonetically valid, and "This is the boy whom I saw yesterday" matches the intended meaning that this is one identified person. So "the" is the best answer.