Could you tell me whether it is adjective or verb at a sentence, "The mall is located..."

I am reading a vocab book to learn English.

There is a example sentence.

That is, "The mall is located his client's long-lost cousin in Mexico."

At the sentence, the 'located', I was sure it was adjective.

But my colleague said, it is verb, because 'located' is not only adjective,

it is also P.P. + verb. So it is verb.

I would like to make it sure.

Thank you very much for your help in advance.

Answer

"Located" is the past participle of the verb "to locate" (meaning to place or to find). So it's a verb form, and it has two uses -- 1) as a participial modifier of nouns, working like an adjective or 2) in combination with some form of the verb "to be" (here "is") to make a verb in the passive voice. I don't understand your example about the mall, so I'll make up my own. Suppose I write

I'm completely lost, until -- finally! -- the mall is located by my car's
GPS.

We can tell this is the passive-voice usage because we can transform the clause into the active voice in three steps:

1. The object of the preposition of agency, "by", (here, "my car's GPS) becomes the subject.


2. The passive becomes the active: "is located" -> "locates"


3. The subject ("the mall") becomes the object.
   
   This gives us

My car's GPS locates the mall.

Now consider the sentence

The mall is located by the river.

Here "located" is a participle that serves as an adjectival complement to "mall," telling us which mall we're talking about. It's the mall down by the river. Note that the same three-step trick won't work. "By" is still a preposition, but it's one of location, telling us where; not agency, telling us who. If we try it anyway, we get

The river locates the mall.

Which makes no sense.