Hopefully this clarifies things, since I was also confused. Slaat af is a form of the afslaan verb http://www.verbix.com/webverbix/go.php?T1=afslaan&Submit=Go&D1=24&H1=124, so now it's understandable to have "slaat rechts/links af".
Also, do not forget that afslaan is the infinitive, which is necessary when using kunnen/hoeven/moeten e.g. Hier moet ik rechts afslaan (I think it's how you write it...).
There has been some confusion on this page.
The Dutch sentence we are given here does NOT use the Dutch verb "afslaan". The verb used is just "slaan".
The word "af" does appear in the Dutch sentence here, but it is not part of the verb "afslaan". Rather, it is part of the adverb "rechtsaf", which means "towards the right".
Instead of "rechtsaf", it is also possible to say just "rechts", which is also an adverb. It means "to the right" (with verbs of motion) or "on the right" (static).
In English there is a slight difference between "toward the right" and "to the right". The phrase "to the right" is more exact, referring to a definite 90-degree turn. The phrase "toward the right" (or "rightwards") is more tentative and approximate.
The same distinction is made in Dutch between "rechts" (90 degree) and "rechtsaf" (approximate).
Reasonable. If you're picky, not excellent.
I tend to treat "taking a right" as limited to an intentional turn in a grid (or otherwise controlled) set up, such that the turn exists, before you "take" it.
Maybe it's a traffic lane, maybe it's a sidewalk, maybe it's a hiking path, maybe it's the entrance to the park--but it's "a right." As in, "take the next right."
But we don't know that the dog is turning right from one street / sidewalk to another, or onto a path. Maybe it's turning a meter right-ish, across the grass, to pee on a bush.
If I were making the decisions (I'm clearly...not) I'd accept "takes a right at," but still prefer the other.
Put the one-word adverb (rechtsaf) before the multi-word prepositional phrase (bij het park).
Also, consider the English. Would you say "The dog turns at the park to the right?" Probably not.
In both languages, you do not usually insert a prepositional phrase in between a verb and an adverb closely associated with that verb.
Bij het park/ at the park - what does geographically exactly mean? He is in the park and turns right inside tge park or he is not in the park but directly next to tge park and turns right tgere(so outside of the park)? Or both can be? - English is not my native language as you probably have found it out already from my question:) thaanx for answer!