AffineRatio - AffineRatio[]

Definition: The affine ratio between 3 colinear points is the number \color{#CC00CC}{m} such that \color{#009900}{C} = \color{#FF0000}{A} + \color{#CC00CC}{m} * \color{#FF0000}{A}\color{#0000FF}{B} . More

Let a, b and c be the y-value of the 3 points A, B and C. Then \color{#CC00CC}{m} = \color{#999900}{n} = \,\, \frac{\color{#009900}{c}-\color{#FF0000}{a}}{\color{#0000FF}{b}-\color{#FF0000}{a}} .

If A, B and C are not colinear, AffineRatio[A,B,C] is undefined.

Notice that if C is between A and B, \color{#CC00CC}{m}< 1.

In the above GeoGebra InterActivity, \color{#009900}{C} is defined as a point on the line \overline{\color{#FF0000}{A}\color{#0000FF}{B}} .

Thus, even if we move A, B or C: \color{#CC00CC}{m}= \,\,AffineRatio[A,B,C] is always defined.

AffineRatio[ <Point>, <Point>, <Point> ]