Min rosa tröja låg i gräset, och hennes orange handduk låg vid sjön.

Because tröja is an en-word.

Swedish uses these possessive forms:

• min with singular en-words
• mitt with singular ett-words
• mina with plurals

So:

• min tröja = my sweater
• mitt hus = my house
• mina tröjor = my sweaters

That is why the sentence has min rosa tröja.

Unlike min / mitt / mina, the word hennes is normally unchanged no matter what kind of noun follows.

For example:

• hennes handduk = her towel
• hennes hus = her house
• hennes böcker = her books

So hennes orange handduk is correct just as it is.

Some Swedish color words are often indeclinable, which means they stay the same instead of changing to match gender or number.

That is why you get:

• rosa tröja
• rosa hus
• rosa tröjor

and similarly:

• orange handduk
• orange hus
• orange handdukar

This is different from regular adjectives such as röd, which do change:

• röd tröja
• rött hus
• röda tröjor

Swedish often prefers a position verb instead of the more general vara.

Here, låg is from ligga, meaning to lie. Since a sweater and a towel are things that normally lie flat, ligga is the natural choice.

Swedish commonly does this:

• boken låg på bordet = the book was lying on the table
• koppen stod på bordet = the cup was standing on the table
• barnet satt på stolen = the child was sitting on the chair

English often just says was, but Swedish is usually more specific.

Låg is the past tense of ligga.

Its basic forms are:

• ligga = infinitive
• ligger = present
• låg = past
• legat = supine/past participle form used in compound tenses

In English, you might translate låg as either:

• lay
• was lying

Swedish does not usually separate those two ideas the way English does, so the context decides which English translation sounds best.

Both can be possible, but they give slightly different pictures.

• i gräset suggests in/among the grass
• på gräset suggests on the grass, more on the surface

So låg i gräset makes the sweater sound as if it was lying among the blades of grass, which is very natural.

Vid means by, beside, or at in the sense of being near something.

So:

• vid sjön = by the lake / at the lakeside

This tells you the towel was near the lake, not in it.

Compare:

• i sjön = in the lake
• vid sjön = by the lake

In Swedish, the definite article is usually attached to the end of the noun.

So:

• gräs = grass
• gräset = the grass

and:

• sjö = lake
• sjön = the lake

This is one of the big differences from English. Instead of putting the before the noun, Swedish often adds a definite ending:

• -et for many ett-words
• -en or -n for many en-words

That is the normal order in Swedish noun phrases like these:

• min rosa tröja
• hennes orange handduk

So the pattern is:

possessive + adjective + noun

Also, after a possessive, Swedish normally uses the noun in its indefinite form, not the definite form. That is why it is:

• min tröja
• not min tröjan

Compare:

• den rosa tröjan = the pink sweater
• min rosa tröja = my pink sweater

Because the sentence contains two full clauses:

1. Min rosa tröja låg i gräset
2. hennes orange handduk låg vid sjön

In Swedish, it is normal to include the verb in both clauses:

• X låg ..., och Y låg ...

English can sometimes omit the second verb in a similar structure, but Swedish usually keeps it, especially in clear, standard sentences like this.