How to Measure the distance of quasars

A Galaxy, which is, placed millions of light year far from earth. How do we measure its distance from us?

n nearby galaxies, we can observe individual stars. Some of these stars are so-called Cepheid variables, which are stars whose total brightness varies over a period of days. By examining such stars that are close enough to the Earth so that their distances can be measured by triangulation, scientists have determined that the average true brightness of a Cepheid variable is related in a simple way to the period of its variation. By observing the period of variation of Cepheid in a distant galaxy, and by observing the apparent brightness of these stars, one can calculate how far away the galaxy is.
The distances to more distant galaxies are determined using a certain kind of supernova, called a type I-a supernova. Such supernovae are very bright and all have about the same true brightness (as was determined by observing such supernovae in galaxies whose distance is known through the Cepheid method). Such supernovae can be identified even in extremely distant galaxies by the characteristics of their light. By observing how bright such a supernova seems to be, one can estimate the distance to the galaxy in which it resides.

Galaxies and quasars are too far away to measure with parallax. So two other methods are used; one is to measure the redshift of the object to determine how fast it appears to be moving away from us. Using Hubble's constant, we can calculate a rough distance. Generally the faster it appears to be moving away, the farther away it us.

Also, certain types of stars (Cephids) are all believed to be the same brightness. The dimmer one appears to be, the farther away it is, as determined by the inverse square of light (twice as far, four times dimmer).