The house------to the old man was built hundreds of years ago.

因为种种原因belong to 是属于某人的意思,但是belong to是动词短语只能做谓语,这句话里已经有 was built 这个谓语了,所以用belonging to 是现在分词做定语, 修饰前面的house,意思是这个老人的房子.

完整是“The house which is belonging to the old man was built hundreds of years ago.”