The correct answer is option 2: different origin and common function.

Analogous structures are body parts or features that appear similar in function but have evolved independently in different species. In the case of wings in birds and bats, both species have developed wings to enable flight. However, the wings of birds and bats have different origins and are structured differently.

Birds have wings made up of feathers, while bats have wings made up of a thin membrane of skin stretched over elongated fingers. The structures of their wings are completely different, but they serve the same purpose of allowing flight.

Option 1, which suggests a common origin and common function, is incorrect because the wings of birds and bats have different origins. Birds are descendants of dinosaurs, while bats are mammals.

Option 3, which suggests a common origin and different function, is also incorrect because the wings of birds and bats have the same function - flight.

Option 4, which suggests different origin and different function, is also incorrect because the wings of birds and bats have the same function of flight, even though they have different origins.

Therefore, the wings of birds and bats are considered analogous structures because they have a different origin but serve the same function.