again...Geometry. pints, lines, collinear.?

Question

**I know I've asked it a couple of times but I messed up and the answers are wrong. •The one who answered both- thanks so much but they did not make sense. I NEED situations.

•How many lines are determined by four points? Consider the situations:all four points are collinear&where three of the four points are collinear. Are there other possible situations?
•I understand what to do... but not exactly how to do it. I am going to ask my teacher for help but... I need the answers for that day so help if you can, thanks so much.

Determine it: 1) where the four points are collinear -and- 2) where three of four points are collinear.
*other possible situations- yes, but what are they? I definitely need to know that part...
•I know that if there are 4 collinear points, then that is one line, because a line continues in each direction.
•Then if it is 3 out of 4 points that are collinear, would it be no line? Wouldn't they just be segments and rays? I NEED the other situations. Thanks.

Answer 1

A st. line can be formed by two points.
Three cases:
1) 4 collinear
2) 3 collinear
3) no collinearity, it means no 3 points are collinear


1)
1 st. line
pt1 pt2 pt3 pt4

2)
3 collinear points makes one st. line
each of the three points of the collinear points can make a st. line with the 4th point which is not collinear with the 3. and so, 3 lines can be formed
==> for 3 collinear points of the 4, we have 1 + 3 = 4 st. lines

3)
the st. lines that can be formed are:
pt1 with pt2
pt1 with pt3
pt1 with pt4
pt2 with pt3
pt2 with pt4
pt3 with pt4

==> 6 st. lines.


* * * * * Explaining second case:

pt1 pt2 pt3 are collinear
pt4

the 4st. lines are:

pt1 pt2 pt3
pt1 pt4
pt2 pt4
pt3 pt4

Answer 2

It takes two points to define a line.

You asked about lines. Then you talked about segments and rays. Your question is unclear. I assume not all points need to be used for an individual line, ray, or line segment.

If all 4 points are collinear, you can form:
- one line
- six rays
- six line segments

If only 3 points are collinear, you can form:
- four lines
- ten rays
- six line segments

If only 2 points are collinear, you can form:
- six lines
- twelve rays
- six line segments

You may have noticed--the number of line segments doesn't change.