1. You must keep your dog on a leash.
2. Your dog is on a leash.
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Is 'on a leash' an adverbial phrase or an adjective phrase in #1 and #2?
Is 'on a leash' an object complement in #1?
It's an adjective phrase modifying or completing the dog, so it's an objective complement. In the second sentence it is a predicate adjective completing the phrase "your dog is..."
It's an adjective phrase, modifying dog
In the first sentence "dog" is the direct object of the verb "keep". In the second, the "dog" is the subject followed by the intransitive verb "is", but still modifies "dog".
BTW, Writeteacher or Ms. Sue may disagree with me. We'll see. :)
As Reed predicted, I disagree with him.
In the first sentence, "on a leash" is an adverb phrase, modifying "keep."
That was my first "impulse", too, but I looked it up in Walsh. You're probably right, but we could argue. LOL
To determine whether "on a leash" is an adverbial phrase or an adjective phrase in sentences 1 and 2, we need to analyze its function.
In sentence 1, "You must keep your dog on a leash," the phrase "on a leash" provides additional information about how the action of keeping the dog should be done. It answers the question of how the dog should be kept — on a leash. In this case, "on a leash" acts as an adverbial phrase modifying the verb "keep." Therefore, it is an adverbial phrase in sentence 1.
In sentence 2, "Your dog is on a leash," the phrase "on a leash" provides information about the state or condition of the dog. It describes the dog and modifies the subject "dog." It is functioning as an adjective phrase because it is acting as an attribute of the subject. Therefore, it is an adjective phrase in sentence 2.
Regarding whether "on a leash" is an object complement in sentence 1, an object complement is a word or phrase that renames or describes the direct object. In this case, the direct object of the verb "keep" is "your dog." However, "on a leash" does not rename or describe the dog explicitly; instead, it describes how the dog should be kept. Therefore, "on a leash" does not act as an object complement in sentence 1.