"Your plate is on the table."
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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.
盘子 itself is an ordinary plate
盘 as part of a compound character like 茶盘 means 'tea tray/plate'. When it's part of a compound, it's usually takes on the meaning of a particular type of a thing
杯子 is a drinking glass, but
玻璃杯 is a glass cup or a drinking glass make from glass Mando doesn't really say 玻璃杯子
茶杯 a tea cup
酒杯 a glass for beer or booze
世界杯 the World Cup
That is just now how Chinese works. Please refer to https://resources.allsetlearning.com/chinese/grammar/Expressing_location_with_%22zai...shang/xia/_li%22 for more information.