Suppose that we suddenly discovered that all these years we'd been wrong about the distance from Earth to the Sun, and it is actually 10% greater than we'd thought. How would that affect our estimate of the distance to the Andromeda Galaxy

The average distance between the earth and the sun is approximately 93 million miles and it a very large distance. This distance is directly responsible for the existing surface temperature of the earth. If the earth had been closer to the sun then the surface temperature would have increased and if the distance was larger then there would be lower surface temperature. Thus, the distance is an important factor.

According to the given condition, if the distance between the sun and the earth is discovered to be 10% more than the current distance, then the distance from the earth to the Andromeda Galaxy would also have increased by 10%.