Ianua a serva aperitur, et hospes in atrium ducitur.

Latin usually does not use articles like English the or a/an.

So:

• ianua can mean door or the door
• serva can mean slave-girl, a slave-girl, or the slave-girl
• hospes can mean guest or the guest

You figure out which one is meant from the context. That is very normal in Latin.

Here are the forms:

• ianua — nominative singular
• a serva — ablative singular after a
• hospes — nominative singular
• in atrium — accusative singular after in

Why these cases?

• ianua is the subject of aperitur
• serva is the person doing the action in a passive sentence, so Latin uses a/ab + ablative
• hospes is the subject of ducitur
• atrium is the place into which the guest is led, so in takes the accusative for motion toward/into

The ending -tur is a very common sign of the third person singular passive in the present tense.

So:

• aperit = he/she/it opens
• aperitur = he/she/it is opened

and

• ducit = he/she/it leads
• ducitur = he/she/it is led

In this sentence:

• ianua aperitur = the door is opened
• hospes ducitur = the guest is led

In a passive sentence, the person who performs the action is often called the agent. Latin commonly expresses the agent with a or ab plus the ablative.

So:

• a serva = by the slave-girl

This is why the sentence says:

• ianua a serva aperitur = the door is opened by the slave-girl

A useful rule:

• a/ab + ablative = by someone in a passive sentence

Also, a and ab are just two forms of the same preposition. Very roughly:

• ab is used before vowels and often before consonants too
• a is often used before consonants

So a serva is exactly what you would expect.

Because the Latin clause is passive.

In English too, compare:

• active: The slave-girl leads the guest
• passive: The guest is led

In the passive version, the guest becomes the subject of the sentence. Latin does the same thing.

So in:

• hospes in atrium ducitur

hospes is nominative because it is the grammatical subject of ducitur, even though it is the one being led.

Because Latin uses:

• in + accusative for motion into/toward
• in + ablative for location in/on

So:

• in atrium = into the atrium
• in atrio = in the atrium

Here the guest is being led into the atrium, not simply being located there, so the accusative atrium is correct.

Latin word order is much more flexible than English word order because Latin shows grammatical relationships mainly through endings, not position.

English depends heavily on order:

• The slave-girl opens the door is different from
• The door opens the slave-girl

Latin endings make the roles clearer, so words can move around more freely for style or emphasis.

In this sentence:

• Ianua a serva aperitur, et hospes in atrium ducitur

the basic meaning is clear from the forms:

• ianua and hospes are subjects
• a serva is the agent
• in atrium shows direction

A Latin writer can often place words where they sound best or where they give emphasis.

Et simply means and.

It joins the two clauses:

• Ianua a serva aperitur
• hospes in atrium ducitur

So the sentence has two linked actions:

1. the door is opened by the slave-girl
2. the guest is led into the atrium

The two verbs are:

• aperitur from aperio, aperire = to open
• ducitur from duco, ducere = to lead

Their active and passive forms here are:

• aperit = opens

• aperitur = is opened

• ducit = leads
• ducitur = is led

A learner often needs to recognize that the form in the sentence may look different from the dictionary form, especially when the verb is passive.

Yes. Serva is a feminine noun meaning slave-girl or maidservant.

That matters mainly for vocabulary and agreement elsewhere in Latin. In this sentence, it tells you the agent is female:

• a serva = by the slave-girl

If the agent were male, you might expect a servo instead, from servus.

Because hospes is the subject of the passive verb ducitur, so it must be in the nominative.

If the sentence were active, then guest would be the direct object, and Latin would use the accusative:

• active: serva hospitem in atrium ducit = the slave-girl leads the guest into the atrium

But in the passive sentence:

• hospes in atrium ducitur = the guest is led into the atrium

the guest becomes the subject, so Latin uses hospes, not hospitem.