2 points determine a line.
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No, 2 points define a line, 3 points define a plane.
Two distinct (different) points are needed to determine a line.
Yes since 3 non-collinear points determine a plane. Of course one can take any two of the three points and draw a line between them. There are an infinite number of planes going through this line. Now pick on more point, not on the line, and those three points uniquely determine a plane.
In coordinated geometry the points on a straight line will determine its equation.
Where are the points!