2nd October 2019

16

# Do any three points always sometimes or never determine a plane?

Never; Postulate 2.7 states if two planes intersect, then their intersection is a line. SOLUTION: The points must be non-collinear to determine a plane by postulate 2.2. Therefore, the statement is sometimes true. Three non-collinear points determine a plane.

Likewise, people ask, why any two points are collinear?

Collinear. Three or more points , , , , are said to be collinear if they lie on a single straight line . A line on which points lie, especially if it is related to a geometric figure such as a triangle, is sometimes called an axis. Two points are trivially collinear since two points determine a line.

Can a line and a point can be collinear?

Points that lie on the same line are called collinear points. If there is no line on which all of the points lie, then they are noncollinear points.

Can a line be coplanar and collinear?

Collinear points are all in the same line. Coplanar points are all in the same plane. So, if points are collinear then we can choose one of infinite number of planes which contains the line on which these points lie => so they are coplanar by definition.