Learn Hardcore Polish: Ten obrazek leży na biurku. - This picture is lying on the desk.

ten obrazek = this picture (masculine, singular, nominative)
to is usually:
- a standalone pronoun: To jest obrazek. = This/It is a picture.
- the neuter form used with neuter nouns: to biurko (this desk).

You cannot say to obrazek in this sentence, because obrazek is masculine, and the masculine nominative form is ten, not to.

How do I know that ten is the right form of “this” for obrazek?

You look at the gender of the noun.

obrazek is a masculine noun.
For a masculine noun in the nominative singular, you use ten:
- ten obrazek – this picture
- ten telefon – this phone

Compare with other genders:

Feminine: ta książka – this book
Neuter: to biurko – this desk

So: masculine → ten, feminine → ta, neuter → to (in nominative singular).

Why do we use leży instead of just jest for “is” here?

Polish often uses specific position verbs instead of the general verb być (to be).

leżeć = to lie / to be in a lying position
leży = is lying / lies

So:

Ten obrazek leży na biurku.
Literally: This picture lies on the desk. (i.e., it is in a lying position on the surface.)

You can say:

Ten obrazek jest na biurku.
This is grammatically correct and means This picture is on the desk, but it is less specific about the position.
Using leży is more natural when something is lying flat on a surface.

What is the full conjugation of the verb leżeć in the present tense?

Present tense of leżeć (to lie, be lying):

ja leżę – I am lying
ty leżysz – you are lying (sg., informal)
on/ona/ono leży – he/she/it is lying
my leżymy – we are lying
wy leżycie – you are lying (pl.)
oni/one leżą – they are lying

In the sentence Ten obrazek leży na biurku, leży is 3rd person singular (it).

Why is it na biurku and not na biurko?

The preposition na can take two different cases:

Locative (miejscownik) – when something is at/on a place (no movement):
- Ten obrazek leży na biurku. – The picture is lying on the desk.
  → biurku is locative (singular of biurko).
Accusative (biernik) – when there is movement onto a surface:
- Kładę obrazek na biurko. – I am putting the picture onto the desk.

So:

Where is it? → na biurku (locative)
Where do you put it? → na biurko (accusative)

What case is obrazek in, and why?

In Ten obrazek leży na biurku, the noun obrazek is in the nominative case (mianownik), because it is the subject of the sentence.

Who/what is lying on the desk? → obrazek
The answer to this question is in the nominative case.

Form:

Nominative singular: obrazek
With the demonstrative: ten obrazek (this picture)

What case is biurku, and what is the base form of that word?

The base form (dictionary form) is biurko – desk (neuter noun).

In the sentence Ten obrazek leży na biurku:

biurku is in the locative case (miejscownik), singular.

Many prepositions in Polish require locative when they show location, including:

na (on)
w (in)
przy (by, near)

Examples:

na biurku – on the desk
w pokoju – in the room
przy oknie – by the window

Can I change the word order? For example, can I say Na biurku leży ten obrazek?

Yes, Polish word order is quite flexible, and both are correct:

Ten obrazek leży na biurku.
Neutral: This picture is lying on the desk.
Na biurku leży ten obrazek.
More like: On the desk, there is this picture. → This emphasizes where it is (the desk) or that something is on the desk.

Other possible (though more marked) orders:

Na biurku ten obrazek leży. (stylistic, poetic, or to stress that it is this picture that is lying there)

Polish uses word order mainly to show emphasis and information structure, not basic grammar like English does.

What is the difference between obrazek, obraz, and zdjęcie?

All three can be related to pictures, but they are not identical:

obrazek
- literally a small picture; often a drawing, illustration, cartoon, or a small image.
- also used informally for a picture in general, especially something not very large or not very formal.
obraz
- usually a painting, especially an artwork that hangs on a wall.
- can also mean image in certain contexts.
zdjęcie
- a photograph.

So:

a framed painting: obraz
a photo: zdjęcie
a small drawing in a children’s book, an icon, simple image: obrazek

Does ten work like “the” or “a” in English? Where are the articles?

Polish does not have articles like a/an or the.

The basic noun obrazek could mean:
- a picture
- the picture depending on context.

The word ten adds the meaning this (and sometimes functions a bit like that specific in English):

obrazek leży na biurku – a/the picture is lying on the desk.
ten obrazek leży na biurku – this picture is lying on the desk.

So ten is not a general article; it is a demonstrative (this), used for pointing out a particular item.

How would I say “These pictures are lying on the desk” using this pattern?

You need the plural forms:

obrazek (sg.) → obrazki (pl.)
ten (this, masc. sg.) → te (these, non-masculine-personal pl.)
leży (sg.) → leżą (pl.)

Sentence:

Te obrazki leżą na biurku.
= These pictures are lying on the desk.

Could I use another preposition instead of na here, like przy or w?

For this meaning, na is the natural choice, because the picture is on the surface of the desk.

na biurku – on the desk (lying/standing on the top surface)
przy biurku – by the desk / at the desk (near it, e.g. sitting at the desk)
w biurku – in the desk (inside a drawer or compartment)

So:

Ten obrazek leży na biurku. – The picture is lying on the desk. ✔ You generally would not say:
Ten obrazek leży przy biurku. (would suggest it’s next to the desk)
Ten obrazek leży w biurku. (would suggest it’s inside the desk)