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Centric stretching

Centric stretching is a mapping. A centric stretching with the stretching centre Z and the stretching factor (similarity factor) k transforms a figure F into a similar one - https://domyhomework.club/ . The stretching centre Z is a fixed point and every straight line through Z is a fixed line of the mapping.

The centric stretching of a figure is already unambiguously determined by the specification of Z and k, since the image point P' must lie on the ray of Z through P.

If k = 1, then it is an identical image.

If k = - 1, the figure "falls" to the other side of Z without changing the length of the line. This is a point reflection.

If |k| > 1, the figure is enlarged; k is then also called the stretch factor.

If |k| < 1, the figure is reduced; k is then also called the compression factor.

Construction of a triangle with a centric stretching (Z; k) with k = 2:

From an arbitrarily chosen Z, the rays of Z are drawn through the vertices of the triangle ABC.

The line length ZA (average) is determined and multiplied by the stretching factor k - https://domyhomework.club/math-homework/ . The line length ZA' (average) is obtained. The line length ZA' (average) is obtained, subtracted from Z and the point A' is obtained. The image points B' and C' are constructed analogously. The image points are connected in the original order.

For each centric stretching the following properties apply:

- The image of a straight line is again a straight line.

- Two mutually parallel straight lines have mutually parallel straight lines as their image.

- The image of a line is a line parallel to it.

- Two line lengths each form the same ratios as their image line lengths.

- Original and image angles are equal.

- The image of an n-corner is again an n-corner.

A centric stretching can also be described as a scaled enlargement or reduction of an original. The stretching factor k is then called scale - geometry homework help . The scale k indicates the ratio of the image stretch length to the original stretch length.

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