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Can I use the word "extreme" to mean the outmost point on a plot?

Wiktionary has the following definition of "extreme":

  1. Of a place, the most remote, farthest or outermost.

Does that mean I could write something like this?

Find the line between the two extreme points.

Line between the two outmost points

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In mathematics, there is a technical term extremum (plural extrema) which refers to a minimum or maximum. Your particular example does not involve the minimum and maximum of a graph, which is usually how extremum is used, but it may be appropriate in slightly different situations.

In your particular example I might use the word distant, as in "the two most distant points". Alternatively, if you want to be very clear and precise and don't mind being wordy, you could say "those two points having the greatest distance between them". This is what I would write if it was part of a mathematical proof.

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That works, and will probably be understood, though it's not common to use "extreme" that way.

As an alternative, you could say,

Find the line between the two furthest points.

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