Anything you like. You could use letters from the Roman or Greek alphabets, numbers, of even give it a human name for a label.
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Your question lacks context. However, it is possible to label a point as point E on any plane you like. The letter is freely available.
Since a Line has only one dimention LENGTH, the only way to identify a point on it is to measure its distance from a known point ... usually on end or the other.
Which label belongs in the area marked Z?
Find the two points and subtract them with X - X and Y - Y. For example: Point A: (1, 2) Point B: (3, -2) Midpoint = (-2, 0). Or you can find the middle point of the line and label the coordinates.
Yes you can label a triangle My daughter is in 3rd and she learned last week how to label triangles.