Magistra quaerit discipulam quae hanc sententiam in linguam Latinam recte transferat.

Because discipulam is the direct object of quaerit.

Here quaerit means is looking for / seeks, so the person being sought is put in the accusative:

• magistra = the teacher (subject, nominative)
• discipulam = the female student (direct object, accusative)

So the basic structure is:

• Magistra quaerit discipulam = The teacher is looking for a female student

Latin quaerere can mean several related things, including to seek, to look for, and sometimes to ask.

In this sentence, quaerit discipulam most naturally means she is looking for a female student, because:

• the verb takes a direct object, discipulam
• the rest of the sentence describes the kind of student she wants to find

If Latin wanted to say asks a student, the context would usually make that clearer in a different way. Here the sentence is about searching for a suitable student, not asking one a question.

Because quae is the subject of transferat inside the relative clause.

A relative pronoun has to do two jobs at once:

1. it must agree with its antecedent in gender and number
2. it gets its case from its role in its own clause

Its antecedent is discipulam, which is:

• feminine
• singular

So the relative pronoun must also be feminine singular.

Then we ask: what is it doing in its own clause?

• quae ... transferat = who ... may/would translate

Since it is the subject of transferat, it must be nominative:

• feminine singular nominative = quae

If it were quam, that would be accusative, and that would mean the pronoun was the object of the verb, which it is not.

It refers to discipulam.

So:

• discipulam quae ... transferat = a female student who ... may/would translate

Even though discipulam is accusative in the main clause, the relative pronoun becomes quae because it is nominative in the relative clause.

Because this is a very common Latin construction after words like quaerit when someone is looking for a person of a certain sort.

So the sentence does not simply mean:

• The teacher is looking for the student who translates this sentence correctly
  as if a specific student were already known

Instead it means more like:

• The teacher is looking for a student who would/could correctly translate this sentence into Latin
• The teacher is looking for some student capable of doing this

This is often called a relative clause of characteristic, and Latin normally uses the subjunctive in that kind of clause.

So:

• quae ... transferat = who would/might/can translate ... not just
• quae ... transfert = who translates ... as a simple fact

Not exactly in the same way as a plain purpose clause with ut, but it is closely related in idea.

The main point is that the teacher is seeking the kind of student who can do something. That is why many grammars call this a relative clause of characteristic.

You can think of it in English as:

• a student who would translate ...
• a student able to translate ...
• a student to translate ...

So the subjunctive helps show that the student is not being identified as an already-known individual, but described by the quality or function the teacher wants.

Because it is the direct object of transferat.

The verb transferre means to transfer, translate, and the thing being translated is put in the accusative.

So:

• hanc = this (feminine singular accusative)
• sententiam = sentence (feminine singular accusative)

Together:

• hanc sententiam = this sentence

With transferre, Latin very often says translate something into a language with in + accusative.

So:

• in linguam Latinam = into the Latin language
• transferre in linguam Latinam = to translate into Latin

This is a standard idiomatic way to say it.

Could Latin sometimes use something shorter? Yes, but with transferre, in linguam Latinam is very natural and explicit.

Notice also that in here means into, so it takes the accusative:

• linguam Latinam = accusative

Because it agrees with linguam, which is a feminine noun.

• lingua = language, tongue (feminine)
• Latinus, Latina, Latinum = Latin

So:

• linguam Latinam = the Latin language in the accusative singular feminine

The adjective must match the noun in:

• gender
• number
• case

Recte is an adverb, and it modifies transferat.

So it tells us how the student would translate:

• transferat = translates / may translate
• recte transferat = translates correctly / may translate correctly

It does not modify sententiam or linguam Latinam. It describes the action of translating.

Because both the teacher and the student are female.

• magistra = female teacher
• discipulam = female student
• quae = who, referring back to discipulam

So the sentence is specifically about a woman teacher looking for a girl/female student.

If the student were male, the sentence would change:

• discipulum quem ... transferat

The word order is normal and natural, but Latin word order is much freer than English word order.

The sentence is arranged as:

• main clause first: Magistra quaerit discipulam
• then the relative clause describing discipulam: quae hanc sententiam in linguam Latinam recte transferat

Latin can do this because the endings show the grammatical roles clearly.

So even if the order changed, the forms would still tell you what each word is doing. But this order is a straightforward way to present the idea:

• first, the teacher is looking for a student
• then, Latin tells you what kind of student

Not automatically wrong in all imaginable contexts, but it would change the sense.

• quae ... transfert would sound more like who translates ..., describing a known or definite person as a matter of fact
• quae ... transferat suggests who would/could translate ..., the kind of student the teacher is looking for

Because the main verb is quaerit and the student is not yet identified, the subjunctive transferat is the expected and idiomatic choice.