lambda meaning on the expression $λA+(1−λ)B$

Question

I was reading an article regarding a convex function and my question is regarding the meaning of the following definition. $λA+(1−λ)B$. 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: $Point A=(50,150); Point B=(150,50)$ and he defined this equality $λA+(1−λ)B=(150−100λ,50+100λ)$ 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 $λA+(1−λ)B$ and why he expressed the two points in that way. I hope I am clear with my question.

Answer 1

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

When $\lambda=0$, you are at $B$.

When $\lambda=1$, you are at $A$.

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