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Definition: The affine ratio between 3 colinear pointsA, B and C is the number m=AffineRatio[A,B,C] such that C=A+m*ABMore
If AB be a line segment and C a point on AB. The affine ratio of A, B and C is the ratio m= |AC|/|AB|. That is,m tells us "how far" C is along the segment AB.
Let aY, bY and cY be the y-values of the 3 points A, B and C. Then
Because A, B and Care colinear, we have similar triangles and it also follows that:
If A, B and C are not colinear, AffineRatio[A,B,C] is undefined.
GeoGebra InterActivity:Directions
1. Click and drag the points. A and B move freely, but C will only move along the line.
2. In the Algebra View (at left):
Roll your mouse over line p to see the definition of p=Line[A,B].
Then roll your mouse over point C to see the definition of C=Point[p].
This ensures that A, B and C are colinear. 3. Finally, check out how m changes as C moves along line p.
In the above GeoGebra InterActivity, C is defined as a point on the line AB so A, B and C are always colinear.
Thus, even if we move A, B or C, m=AffineRatio[A,B,C] is always defined.
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