Although it is highly unlikely to happen, 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 distance to the andromeda galaxy is also 10% greater.

Explanation:

The Andromeda galaxy also called by the M31 the spiral galaxy i.e 2.5 billion light-years from the earth and is the nearest major galaxy to our galaxy. Its mass is almost the same as that of the Milky way i.e One trillion solar masses. And is more in width than our galaxy by 20 to 50 %. Both these galaxies are known to merge in about 4.5 billion years form now merging into an elliptical galaxy. This galaxy was formed about 10 billion years ago. The distance measuring techniques like the surface brightness techniques have been used along with the Cepheid variables which estimate the distance as 2.51 ± 0.13 million light-years.