Pater materque in atrio sedent.

In Latin, -que is an enclitic, meaning it is added to the end of a word and means and.

So:

• materque = mother and
• together with pater, it means father and mother

This is a very common Latin way to join two words, especially two closely connected nouns.

So pater materque literally looks like father mother-and, but in normal English we understand it as father and mother.

Yes. Latin can use either:

• pater et mater
• pater materque

Both mean father and mother.

A rough difference is:

• et is a separate word meaning and
• -que often feels a little more tightly linking, like the two words belong together as a pair

In many simple sentences, both are possible.

That is the normal pattern. -que usually attaches to the second of the two joined words:

• pater materque = father and mother
• not usually paterque mater

So Latin often builds the pair like this:

• first item
• second item + -que

That is just the standard idiom.

Latin does not have articles like English the and a/an.

So:

• pater can mean father or the father
• mater can mean mother or the mother
• atrium can mean atrium or the atrium

You understand from context whether English should use the, a, or no article at all.

Atrio is ablative singular.

Its dictionary form is:

• atrium, atrii = atrium, hall, central court

With the preposition in, Latin often uses:

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

Here the meaning is location, not movement:

• in atrio = in the atrium

So the ablative atrio is exactly what we expect.

No. This is an important Latin pattern.

• in + ablative = in / on somewhere
  
  • in atrio = in the atrium
• in + accusative = into / onto somewhere
  
  • for example, in atrium = into the atrium

So the case after in helps show whether the idea is location or motion toward.

Because together they form a compound subject:

• pater materque = father and mother

Even though each noun is singular by itself, together they mean two people, so the verb must be plural.

That is why Latin uses:

• sedent = they sit / are sitting

not a singular verb.

Sedent is:

• 3rd person plural
• present tense
• from the verb sedeo, sedere = to sit

So sedent means:

• they sit
• or they are sitting

Latin present tense often covers both simple present and present progressive in English.

Because the verb ending already tells you the subject is they.

In sedent, the ending -nt marks 3rd person plural.

So Latin does not need to say they separately unless it wants extra emphasis.

This is very common in Latin: the verb ending often gives enough information by itself.

Latin word order is much more flexible than English word order because the endings show the grammatical relationships.

So Pater materque in atrio sedent is perfectly normal Latin. Putting the verb at or near the end is very common.

The sentence is arranged neatly like this:

• pater materque = the subjects
• in atrio = where they are
• sedent = the verb

Latin could sometimes rearrange these words for emphasis, but this order is natural and straightforward.

Their dictionary forms are:

• pater, patris = father
• mater, matris = mother

Both are third-declension nouns.

In this sentence, they are in the nominative singular, because each one is part of the subject:

• pater = father
• mater = mother

Even though the whole subject is plural in meaning, each noun itself stays singular.

A common classroom pronunciation would be something like:

• PAH-ter mah-TER-kweh in AH-tree-oh SEH-dent

A few helpful points:

• -que is pronounced roughly kwe
• tr in atrio is pronounced clearly
• c is never soft here; but there is no c in this sentence anyway
• e in sedent is pronounced like eh, not like English ee

If you are using restored classical pronunciation, that guide is close enough for a beginner.