Every line and every line segment of >0 length has an inifinite amount of unique points.
Socratic Explaination:
consider ...
- There are 2 distinct points defining a line segment.
- Between these 2 distinct points, there is a midpoint.
- The midpoint divides the original segment into 2 segments of equal length.
- There are 2 distinct points used to define each segment.
- Between these 2 distinct points, there is a midpoint for each segment.
- These midpoints divide the segments into smaller segments of equal length.
- repeat until throughly beaten
This leads to a description of an infinite amount of points for any given line segment.
This does not describe all the points of a line segment. Example: the points 1/3 of the distance from either of the the original 2 points are approached but never hit.
Please, feel free to rephrase this explanation. I know it's sloppy.
2
Two distinct (different) points are needed to determine a line.
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.
A plane can be determined by three points, as long as the three points do not lie along a single line.
A line has an infinite amount of points.
2
Two distinct (different) points are needed to determine a line.
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.
2
It takes exactly 2 distinct points to uniquely define a line, i.e. for any two distinct points, there is a unique line containing them.
A plane can be determined by three points, as long as the three points do not lie along a single line.
Unique line assumption. There is exactly one line passing through two distinct points.
In order to draw a straight line, two unique ordered pairs are needed. This is because two unique points determine a line and an ordered pair represents a point.
A set of three points not on the same line are points that define a unique plane.more than three points not on a plane are in a space (volume).
A line has an infinite amount of points.
A plane can be determined by three points that are not on the same line. These three non-collinear points define a unique flat surface in three-dimensional space. Any additional points in the same plane will also lie on that surface, but the three points are sufficient to establish the plane's existence.
In plane geometry, two points determines or defines one unique line.