"Did you see the family playing at the beach?"
Translation:Så du den lekende familien på stranden?
Did you see the family playing at the beach? = Så du familien som lekte på stranden? (/Så du familien lekende på stranden?*)
The most natural translation for "the family playing at…" is "familien som lekte på…". The Norwegian phrase "den lekende familien" would be "the playfull family" or maybe "the playing famliy".
Here, the translation suggested by DL (Did you see the family playing at the beach? = Så du den lekende familien på stranden?) is simply not correct.
Hm... so even if the participle is used as part of a predicate, it's placed in the adjective position? I keep reading this as, "there is a family who plays a lot, and you saw them at the beach." Or replace it with "singing" for example: den syngende familien reads to me like the von Trapps were at the beach, as opposed to just some family singing (which feels like it should be den familien syngende)...
Is there a way to distinguish a (present or otherwise) participle used as a permanent quality (like "playful") versus a current state (like "playing [at the time]")? By "treated as an adjective", do you mean that a present participle will always be the former rather than the latter, or just that it will be positioned like an adjective in a sentence?
The Norwegian sentence could mean either permanent or current state, so context would be helpful if you wanted to distinguish these.
The sentence is somewhat unnatural in Norwegian, it would be more common to say "Så du familien som lekte på stranden?"(Did you see the family who played at the beach?)
Present participles behave just like adjectives in Norwegian, so it should be positioned as one. They can't be used as in English: "I am playing" != "Jeg er lekende"(which makes no sense to say in Norwegian).