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I'm going through coordinate geometry chapter and I cannot understand where the formula below comes from.

Let $X$ and $Y$ be distinct point. The line from $O$ to $X-Y$ is parallel to line from $Y$ to $X$. A point on the line from $Y$ to $X$ is of the form:

$$P = Y + a(X - Y) = aX + (1 - a)Y,$$

where $a$ is a real number.

MarianD
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bluecat
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  • Is it clear to you that $P= aX + (1-a)Y$, where $X$ and $Y$ are points and $a \in \mathbb{R}$, is a straight line? When that's clear, you can check what happens when $a=0$ and when $a=1$, and you'll see that it's indeed a line that passes through $X$ and $Y$. – Matti P. Aug 21 '19 at 10:19
  • For $a=0$, $P=Y$ and for $a=1$, $P=X$. –  Aug 21 '19 at 10:27

1 Answers1

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The following diagram should help you visualize the relationship of all the points.

enter image description here

As you can see in the diagram, the line from $O$ to $X-Y$ is parallel to the line from $Y$ to $X$ and the point $P$ on this line is just $P=Y+Z$, with $Z= a(X-Y)$.

Quanto
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