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Simple ratio

From Encyclopedia of Mathematics
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of three points $M_1,M,M_2$ on a straight line

The number $\lambda$ such that

$$\overline{M_1M}=\lambda\overline{MM_2}$$

One says, moreover, that $M$ divides the segment $M_1M_2$ in the ratio $\lambda$. If $(x_1,y_1)$ and $(x_2,y_2)$ are the coordinates of $M_1$ and $M_2$, then the coordinates of $M$ are

$$x=\frac{x_1+\lambda x_2}{1+\lambda},\quad y=\frac{y_1+\lambda y_2}{1+\lambda}.$$

The simple ratio is an invariant of affine transformations.

How to Cite This Entry:
Simple ratio. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Simple_ratio&oldid=12601
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article