"Your plate is on the table."
In modern Chinese, the proposition is always after the object. And here 上 means the proposition "on".
在 has two meanings. If it is followed by a verb, it is the continuous marker. If it is followed by a prepositional phrase, it is the verb "locate".
在桌子上 = locate (be) on the table
在上桌子 = getting upon the table (上, as a verb, means "get upon")
盤子 like many nouns with only one character (比如: 椅子，桌子，房子，兒子/儿子，帽子，鬍子，杯子，叉子，筷子) is followed by 子, called the noun suffix, when the noun appears by itself.
I think it helps to resolve ambiguity inherent in speaking (none of those would be ambiguous when written).
Often when those same nouns appear in compounds the 子 is dropped.