Question

A star is located at a distance of about 100 million light years from Earth. An astronomer plans to measure the distance of the star by the parallax method. Which of these statements best explains why the astronomer's method of measuring the star distance is inappropriate?
a. At large distances, a red shift in the star's spectrum causes incorrect measurements.
b. At large distances, a blue shift in the star's spectrum causes incorrect measurements.
c. The parallaxes beyond a few thousand light years are too large to be used to measure distances.
d. The parallaxes beyond a few thousand light years are too small to be measured with common instruments.

Answer 1

d. The parallaxes beyond a few thousand light years are
too small to be measured with common instruments.

I'm not sure that parallax can even be used out to a few
thousand light years.

The NEAREST star to Earth has the BIGGEST parallax.
The star is Alpha Centauri.  It's only 4 light years away
from us, and its parallax is  0.000206 of a degree !
I have no idea how astronomers can measure angles
so small ... and that's the BIGGEST parallax angle of
ANY star.