You need two.
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a line has to have at least 2 points.a plane has to have at least 3 points.______________It takes two points to define a unique line in Euclidean space. But every line and every line segment contains infinitely many points. The same is true for planes in Euclidean space. You need at least 3 points to define a unique plane, but every plane containes infinitely many points and infinitely many lines or line segments.
You need to know the total available points. 50 out of 100 points is 50%. 50 out of 80 points is 62.5%
a plane is any plane surface it usually have 3 or 4 points * * * * * You need only three points provided they are not collinear. And most planes have infinitely many points although there are geometries with only a finite number of points.
Hoe
Do I have a compass to use or not ? It's not clear from your question, but since you mentioned it at the end of the question, I'll assume that I do have a compass, and in that case, I only need one straight-edge. 1). Plant the compass on one end of the line segment, open it to more than half the length of the segment, draw a long arc that crosses the segment. 2). Keep the same opening, pick up the compass. 3). Plant the compass on the other end of the segment, draw another long arc that crosses the segment. 4). Sell the compass. 5). The two arcs intersect at two points on opposite sides of the segment. With your straight edge, draw a line between these two points. That line is the perpendicular bisector of the original segment.