Stretching in the coordinate system
Compute images of points and lines under a Zentrische Streckung with the vector rule, find k, and find the Schwerpunkt of a triangle.
📖 Start here: read the steps of the “Lesson” in order (1, 2, 3 …) and answer each question. Then continue with “Practice”.
- France: grade 8
- Germany: grade 9
- Syria: grade 6
- Ukraine: grade 9
Guide
A Zentrische Streckung has a centre Z and a Streckungsfaktor k. With Z(0|0) the point P(x|y) goes to P′(k · x | k · y): the vector ZP′ is k times the vector ZP.
For |k| > 1 the figure is enlarged, for |k| < 1 reduced, for k < 0 it is also turned by 180° about Z; k = –1 is the Punktspiegelung. A line is mapped onto a parallel line.
The Schwerpunkt of a triangle is S = ⅓ · (A + B + C). It divides each Seitenhalbierende in the ratio 2 : 1. This studio belongs to the Realschule syllabus (Jgst. 9).