Learn Hardcore Greek: Η απόσταση από τον καναπέ μέχρι το τραπεζάκι είναι ένα μέτρο. - The distance from the sofa to the coffee table is one meter.

απόσταση (distance) is a feminine noun.
Since it is the subject of the sentence, it appears in the nominative case.
So you get Η απόσταση = “the distance”.

If it were plural, you would say Οι αποστάσεις (the distances), with Οι as the feminine plural nominative article.

Why do we use both από and μέχρι here? What is the function of this pair?

The pair από … μέχρι … means “from … to …” in a spatial or temporal sense.

από = from
μέχρι = until / up to / to

So από τον καναπέ μέχρι το τραπεζάκι literally means “from the couch to the small table”.
This is a very common and natural way to express distances or ranges in Greek.

Why is it από τον καναπέ and not από ο καναπές or something similar?

Several things are going on here:

Case:
- Prepositions like από are typically followed by the accusative case.
- ο καναπές (the couch, nominative) becomes τον καναπέ in the accusative.
Article form:
- Masculine nominative singular: ο καναπές (subject form)
- Masculine accusative singular: τον καναπέ (after a preposition, or as a direct object)

So after από, you must say τον καναπέ, not ο καναπές.

Why does καναπές end in -ές but in the sentence it appears as καναπέ without the final ς?

καναπές is a masculine noun whose nominative form ends in -ές:

Nominative (subject form): ο καναπές
Accusative (after prepositions/objects): τον καναπέ

In the sentence, καναπέ appears after από, so it must be in the accusative case, and that form drops the final -ς.
This is normal for many masculine nouns of this type:

ο καφές → τον καφέ
ο μαθητής → τον μαθητή

Why is it μέχρι το τραπεζάκι and not μέχρι του τραπεζιού?

Two separate points:

Case after μέχρι
In modern Greek, μέχρι (meaning up to / until / to) is normally followed by the accusative.
- So you say μέχρι το τραπεζάκι, not μέχρι του τραπεζιού in everyday speech.
Different noun and meaning
- τραπεζάκι (neuter, diminutive) = small table, coffee table
- τραπέζι (neuter) = table
- του τραπεζιού is the genitive of το τραπέζι (of the table), which would not fit here with μέχρι.

So the natural, modern form here is μέχρι το τραπεζάκι (accusative).

What does the ending -άκι in τραπεζάκι mean compared to τραπέζι?

The suffix -άκι often forms diminutives in Greek, usually with the idea of:

something smaller, or
something cute/familiar, or
sometimes both.

So:

τραπέζι = table (neutral in size and tone)
τραπεζάκι = small table, coffee table, side table

Both are neuter nouns, but τραπεζάκι specifically suggests a smaller or side table (like a coffee table in the living room).

Why is it μέχρι το τραπεζάκι with το, but από τον καναπέ with τον?

Because καναπές and τραπεζάκι have different genders:

καναπές is masculine → accusative singular article is τον → τον καναπέ
τραπεζάκι is neuter → accusative singular article is το → το τραπεζάκι

Both are in the accusative case (because they follow prepositions), but the article changes according to the gender of the noun.

Why do we say είναι ένα μέτρο and not είναι ένας μέτρο?

Because μέτρο (meter, unit of length) is a neuter noun:

Neuter singular: το μέτρο
Masculine singular: ο …, e.g. ο φίλος

The numeral one agrees in gender with the noun:

Masculine: ένας (e.g. ένας φίλος)
Feminine: μία / μια (e.g. μία καρέκλα)
Neuter: ένα (e.g. ένα μέτρο)

So you must say ένα μέτρο, not ένας μέτρο.

Could I drop ένα and just say Η απόσταση … είναι μέτρο?

In this specific context, no, that would sound unnatural or incorrect.

For measurements with 1 in Greek, you normally keep ένα:

Η απόσταση είναι ένα μέτρο. = The distance is one meter.

If the number were greater than one, you would use the numeral directly:

Η απόσταση είναι δύο μέτρα. = The distance is two meters.

But for a single unit, ένα is necessary here; just είναι μέτρο does not sound like normal Greek.

Why is μέτρο singular here? How would it change with other numbers?

Greek behaves much like English here:

With 1: use the singular noun
- ένα μέτρο = one meter
With 2 or more: use the plural noun
- δύο μέτρα = two meters
- τρία μέτρα = three meters

So in the sentence, since the distance is one meter, the correct form is ένα μέτρο (singular).

Can I say Η απόσταση ανάμεσα στον καναπέ και στο τραπεζάκι είναι ένα μέτρο instead? Is it equivalent?

Yes, that is a perfectly correct and very natural alternative:

ανάμεσα σε … και … = between … and …

So:

Η απόσταση ανάμεσα στον καναπέ και στο τραπεζάκι είναι ένα μέτρο.
= The distance between the couch and the small table is one meter.

Both versions are normal:

από τον καναπέ μέχρι το τραπεζάκι (from the couch to the small table)
ανάμεσα στον καναπέ και στο τραπεζάκι (between the couch and the small table)

Slight nuance: από … μέχρι … emphasizes the range or span; ανάμεσα σε … και … emphasizes the idea of being between two points, but in practice they overlap a lot in everyday speech.

Why is it στον καναπέ / στο τραπεζάκι in the alternative version, but από τον καναπέ in the original?

Different prepositions and contractions:

In the original:
- από τον καναπέ → από
  - τον καναπέ (no contraction here)
In the alternative with ανάμεσα:
- You use σε (in, at, on) after ανάμεσα: ανάμεσα σε … και …
- σε
  - τον καναπέ contract to στον καναπέ
- σε
  - το τραπεζάκι contract to στο τραπεζάκι

So:

στον = σε
- τον
στο = σε
- το

The contraction is purely phonetic/conventional; grammatically it’s still σε + article.

Is there a difference between μέτρο and μετρό?

Yes, they are completely different words, distinguished by the accent:

μέτρο (accent on μέ) = meter, the unit of length.
μετρό (accent on τρό) = metro / subway.

In the sentence, μέτρο with the stress on the first syllable is used (the unit of distance). Using μετρό here would be wrong and would mean “subway”.