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a triangle is formed by line segments that connect two non-collinear points
False.
If the points are collinear, the number of possible planes is infinite. If the points are not collinear, the number of possible planes is ' 1 '.
If there are n points then the maximum number of lines possible is n*(n-1)/2 and that maximum is attained of no three points are collinear.
To determine if two sets of points are collinear, you can calculate the slopes of the lines formed by connecting the points in each set. If the slopes are equal, then the points are collinear. Another method is to calculate the area of the triangle formed by the three points in each set. If the area is zero, then the points are collinear. Lastly, you can use the determinant of a matrix method to check if the points lie on the same line.