The other girls picked on her because of her size.
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Q1: Is 'picked' a transitive verb or an intransitive verb? Is 'on' a preposition or an adverb? What is the meaning of 'pick' here?
Q2: What other expressions can we use instead of 'picked on'?
It depends on how "pick" is used. In some uses, it is transitive, but in others it's intransitive.
http://www.merriam-webster.com/dictionary/pick
In this sentence, "on" is a preposition, with "her" as its object.
You can also use these expressions:
teased her about...
ribbed her about ...
joked about ...
The verb "to pick" means to pluck something, as one picks a flower, or picks a guitar string, or to pick something up off the floor. It may be a repeated action, as in picking at something that is bothersome. In the case of your sentence, it is an analogy for teasing someone or making fun of someone, usually repeatedly.
"on her" is a prepositional phrase used as an adverb to modify "picked". "On" is always a preposition. With its object, "her", it's a prepositional phrase, which may be an adjective or an adverb phrase. You might say the other girls teased her, or made fun of her.
Q1: 'Picked' is a transitive verb in this sentence because it takes an object, which is 'her'. 'On' is a preposition in this context, indicating the target or place where the action of picking is directed. In this sentence, the word 'pick' means to choose or single out, usually in a negative or bullying way.
Q2: There are several expressions that can be used instead of 'picked on' to convey a similar meaning. Here are a few examples:
1. Bullied: The other girls bullied her because of her size.
2. Teased: The other girls teased her because of her size.
3. Harassed: The other girls harassed her because of her size.
4. Targeted: The other girls targeted her because of her size.
5. Made fun of: The other girls made fun of her because of her size.
These phrases are all interchangeable with 'picked on' and can be used to describe situations where someone is being treated poorly or subjected to negative attention because of a particular characteristic, like their size in this case.