Final answer:
When the distance to the stars is doubled, they appear four times less bright and their angular separation becomes too small for the human eye to resolve, causing them to appear as a single point of light.
Step-by-step explanation:
If the angular separation of two stars is equal to the angular resolution of your eyes, and you then move the stars two times farther away from you, the stars will no longer be resolvable as distinct points of light. This is because increasing the distance without changing the angular separation effectively reduces the angular size of the gap between the stars, making them appear closer together. According to the inverse square law, the intensity of the light received decreases with the square of the distance from the source. If the distance is doubled, the area over which the light is spread increases by a factor of four (2 squared), and thus each star appears four times less bright. Since the stars are now fainter and their apparent proximity has increased, they will blend into a single point of light to your eyes, the correct answer being A) The two stars will look like a single point of light.