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

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SUMMARY

The discussion centers on the collinearity of the points (1,0) and (0,1). It is established that two points always define a straight line, thus confirming that (1,0) and (0,1) are indeed collinear. The conversation emphasizes the importance of defining what a line is before discussing collinearity, as clarity in terminology is crucial for accurate mathematical discourse. The participants highlight that collinearity typically involves more than two points, but in this case, the answer remains straightforward.

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  • Research the mathematical definition of collinearity and its implications in geometry.
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Are the points (1,0) and (0,1) collinear?
 
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Zubair Ahmad said:
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
 
Zubair Ahmad said:
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
 
Zubair Ahmad said:
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.
 

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