Collinear Points: Are (1,0) & (0,1) Aligned?

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In summary, the discussion revolves around the definition of a line and how that relates to the concept of collinear points. Without a clear understanding of what a line is, it is difficult to answer whether (1,0) and (0,1) are collinear or not.

Are the points (1,0) and (0,1) collinear?

Are the points (1,0) and (0,1) collinear?
What is a line to you?

Are you asking if (1,0) and (0,1) are collinear with each other ? - or did you intend to ask a different question?

fresh_42 said:
What is a line to you?
Combination of collinear points

Stephen Tashi said:
Are you asking if (1,0) and (0,1) are collinear with each other ? - or did you intend to ask a different question?
Same as you understood

Combination of collinear points
To say what colinear is, you first have to say what linear is, in this case a line. You cannot define colinear by line and line by colinear at the same time. In this case they would be equivalent and the answer would be trivially yes. So in order to get some meaning to the question, you have to put some truth in it somewhere. That's why I asked, what a line is to you. How can I answer a question about colinear points, if it isn't clear what a line is?

Ok what is a line then

Ok what is a line then

I think you need to answer this first before @fresh_42 can answer your posted question.

Two points define a straight line. So the original question is trivially answered by yes. Usually when asking about collinear, the question involves more than two points.

1. Are (1,0) and (0,1) collinear?

Yes, (1,0) and (0,1) are collinear points because they lie on the same line. In this case, they both lie on the line y = x.

2. What does it mean for points to be collinear?

Collinear points are points that lie on the same line. This means that they share a common straight path and can be connected by a straight line segment.

3. Can collinear points be in any position on a line?

Yes, collinear points can be in any position on a line. As long as they share the same line and can be connected by a straight line segment, they are considered collinear.

4. How can we determine if three points are collinear?

To determine if three points are collinear, we can use the slope formula to calculate the slopes of the lines formed by connecting the points. If all three slopes are equal, then the points are collinear.

5. Why is it important to know if points are collinear?

Knowing if points are collinear can be helpful in geometry and other mathematical applications. It allows us to accurately represent and measure distances and angles, and can also help in problem-solving and making predictions.