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Explain how the expression $tX + (1-t)Y$, $0\le t\le 1$, produces a segment that connects point $X (x_1, y_1)$ with point $Y (x_2,y_2)$.

So I rearranged the problem such that $t(X - Y) + Y$ which I gather the $(X-Y)$ to be changes in $x$ and $y$, but I am struggling with the rest of the explanation.

Ángel Mario Gallegos
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Lindsey
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1 Answers1

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One may look at it like this:

Let $U \,t + V \,(1-t)$ be resulting item you want.It may be a vector, physical quantity etc.

For $t=0 $, you get all U components set, for t=1 you get all V components set, for each and all the components that comprise $U$ and $V, $ whatever the components may be.For $t= \frac12 $ you get their average. The $t$ is a proportioning or weighting parameter to apportion between 0% and 100%. It applies to all set components, like, x,y,z, weight, price..

Narasimham
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  • So, if I am thinking about this visually too, with vectors, then it would create varying triangles proportioned by $t$? – Lindsey Aug 31 '15 at 18:35
  • Yes, proportion the joining line only. If the vectors are OA and OB, then 0.8 OB + 0.2 A when you want to be 80 percent closer to be B. – Narasimham Aug 31 '15 at 18:39