Q: Do 3 points determine a line?

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No, 2 points define a line, 3 points define a plane.

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.

Two distinct (different) points are needed to determine a line.

In coordinated geometry the points on a straight line will determine its equation.

Where are the points!

Related questions

No, 2 points define a line, 3 points define a plane.

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

line.

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.

Two. Two points determine a line. Three points determine a plane.

If you were to have 3 points on the same line, then you would actually not be determining a plane, because there are infinitely many planes that can intersect a given line. But if you have 3 points in the form of the points (or vertices) of a triangle, then you determine a plane in the sense that there is only one possible plane upon which that triangle can be drawn (not including a degenerate triangle, which is equivalent to a line).

In coordinated geometry the points on a straight line will determine its equation.

Where are the points!

A line contains an infinite number of points but it takes only two points to determine a line.

3 points which do not all lie on the same line.

2 points determine a straight line and are always, by definition, collinear.