Question

Where are all points whose coordinates are 2 ?

Answer 1

To distinguish two point sources at the 2 million light-year distance of the Andromeda galaxy, they need to be separated by a distance corresponding to the angular resolution of the observing telescope, which is often thousands of astronomical units or more, limited by the Rayleigh criterion.

Step-by-step explanation:

When discussing the spacing between point sources at the vast distances of intergalactic space, such as the 2 million light-year distance to the Andromeda galaxy, we need to consider the limitations of our observational technology and the resolution it allows. At the distance of the Andromeda galaxy, two point sources would need to be separated by a significant distance to be distinguished as two separate entities. This distance is defined by the resolving power of our telescopes.

The angular resolution of a telescope is the smallest angle between two points that the telescope can discern, and it's often limited by diffraction. Given the wavelength of light and the diameter of the telescope's aperture, we can use the Rayleigh criterion to estimate this angle.

For a telescope to resolve two point sources as separate at the distance of the Andromeda galaxy, they would need to be separated by at least the distance that corresponds to this angular resolution. As technology improves, the minimum distance for resolution gets smaller, but at such distances, we're typically talking about thousands of astronomical units (AU), if not more.

Answer 2

Points whose coordinates are both 2 are located on the vertical line x = 2 in the coordinate plane.

Step-by-step explanation:

The points whose coordinates are both 2 are located in the coordinate plane.

Specifically, they lie on the vertical line x = 2. This line intersects the x-axis at the point (2,0) and extends infinitely in both the positive and negative y directions.