+79 Alice is thinking of a line. How many points on that line does she need to show Bob in order for Bob to know exactly which line she is thinking about?
+1008 Just two. If you only do one, then it can be in any direction.
If two, you can figure out the whole line. Three isn't necessary.
if you are looking for a plane then 3 dots, 4 for 4th dimension, etc.
