lambda meaning on the expression خ»A+(1âˆ′خ»)Bخ»A+(1−خ»)B

I was reading an article regarding a convex function and my question is regarding the meaning of the following definition. خ»A+(1−خ»)Bخ»A+(1−خ»)B. I have seen this in different places. In one of them it was referred as the general form of a line which I did not understand well. It is found in this question: How to get Point between two points at any specific distance?. In the example he had two points: Point A=(50,150); Point B=(150,50)Point A=(50,150); Point B=(150,50) and he defined this equality خ»A+(1−خ»)B=(150−100خ»,50+100خ»)خ»A+(1−خ»)B=(150−100خ»,50+100خ») which I really don’t understand why is it. I would like to have a better understanding of what is the meaning of this expression خ»A+(1−خ»)Bخ»A+(1−خ»)B and why he expressed the two points in that way. I hope I am clear with my question.



1 Answer


write \lambda A+(1-\lambda)B=B+\lambda(A-B)\lambda A+(1-\lambda)B=B+\lambda(A-B)

When \lambda=0\lambda=0, you are at BB.

When \lambda=1\lambda=1, you are at AA.

when \lambda\lambda increases, you are moving from B towards AA along the direction of A-BA-B.