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You've basically asked "what is 8 choose 2?", which is 8! / ( 6! * 2! ) or 28.

The two are identical because each pair of points determines a line (since no three points are collinear). Since there are 28 ways to choose 2 items from a set of 8 items, there are 28 possible pairs of points and therefore 28 lines.

Q: How many line are determine by eight points if none of three points are colinear?

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You have to have three or more points to have non-colinear points because any two points determine a line. Noncolinear are NOT on the same line.

To prove that three points are colinear, pick two points and form the equation of the line they describe, and then see if the third point lies on that line.

Any three points anywhere in space can be the vertices of a triangle, as long as all three are not colinear.

No. A trinagle does not require four points, three are sufficient. And any three points, if they are not colinear, must be coplanar.

Not necessarily, eg the three points (0, 0), (1, 1) and (2,0) are not co-linear, but (0,0), (1,1) and (2,2) are. But three points are co-planar, that is they all lie in one plane.

Related questions

Yes, a plane can be uniquely defined by three points as long as the three points are not colinear. (Three points are colinear if there is a straight line that passes through all three points.)

You have to have three or more points to have non-colinear points because any two points determine a line. Noncolinear are NOT on the same line.

To prove that three points are colinear, pick two points and form the equation of the line they describe, and then see if the third point lies on that line.

Any three points anywhere in space can be the vertices of a triangle, as long as all three are not colinear.

No. A trinagle does not require four points, three are sufficient. And any three points, if they are not colinear, must be coplanar.

Not necessarily, eg the three points (0, 0), (1, 1) and (2,0) are not co-linear, but (0,0), (1,1) and (2,2) are. But three points are co-planar, that is they all lie in one plane.

They lie in the same plane, but they don't necessarily have to lie on the same line. Every triangle consists of three points that are coplanar but non-colinear.

Three points can determine a plane but not 3-d space.

No. Three points do. Two points determine a line.

Any 3 points determine a plane.

Triangle: A figure formed by exactly three (non-colinear) points joined by line segments is a triangle. A figure formed by three or more points is generally called a polygon. Of course, if all of the points are co-linear then there is not much of a figure. A polygon has 3 or more sides.

False. Three collinear points determine a line while three non-collinear points determine a plane ( A Triangle)