Question

why did japan become an imperial power in the late 19th century

Answer 1

Japan modernized and adopted Western ways, while China believed in building on its historic strengths.

Answer 2

It was their turn, in a way. All the European countries had already been doing colonies and Imperialism. Japan had kept to itself until Commodore Perry forced them to trade with the world. So Japan learned how to be a leading nation. They copied all the best military and governments of the European powers. Then they put it to work.
Their disadvantage was being a little late to the party and taking over some previously European held areas.
That's what all the powerful countries did. Why wouldn't they do the same.?