How could you tell if a line of islands was formed by a hot spot and tectonic plate movement?

If the island chain is far away from plate boundaries and it is in a direction of the movement of the plate on which it is located, then those are good indicators that they are formed by hot spot volcanism and tectonic plate movement.

Explanation:

There are multiple types of island chains around the world according to the manner in which they have formed. One type is the island chains that have been formed by hot spot volcanism, and their direction has been determined by the movement of the tectonic plate on which they lie. An example of such islands is the Hawaii islands, located in the central part of the Pacific Ocean and the Pacific plate.

The two best indicators that it is this type of islands in question are their location in relation to the plate boundaries and their direction in relation to the tectonic plate movement. If the island chain is located far away from plate boundaries then it means that it is of hot spot origin. If the direction in which the islands are positioned corresponds with the direction of the plate on which they lie means that the plate's movement is determining their direction.

they use tree rings to figure out weather patters.