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They are points where three or more edges meet.
I think the question you mean to ask is, "Do three collinear points make a triangle?" Linear is simply the adjective form of "line", "collinear" is used to describe points that lie on the same line. (Two points not only can be collinear, but always are, so it makes little sense to describe them as such).Collinear points cannot make a triangle, a triangle requires three noncollinear points.
It is the circumcentre of the triangle formed by the three points. Draw the perpendicular bisectors of two of the lines joining the three points. They will meet at the point that is equidistant from the three points.
For example, you might name an angle as "ABC", where "B" is the vertex, and "A" and "C" are points lying on the sides of the angle. If there are additional points on the same sides, you can substitute those points instead.
A triangle? Three lines that intersect in three points.