What is homothecy?

What Does homothecy Mean

The idea of homothecy is used in the field of geometry to refer to the link established by two figures when their corresponding points are aligned at a fixed point . It is, therefore, a correspondence between geometric figures.

The means homotecia from a point fixed known as center or point O . For the homothetic points , distances are multiplied by a common factor : thus, each point P , corresponds to a point P ' , both aligned with the O point .
The so-called homothetic points are the points transformed by multiplying the original points by the common factor. These homothetic points are aligned with point O and with segments that are parallel to each other.

What homothecy allows is to transform a figure into another similar , but not congruent. The relationship assumes that the figure obtained is smaller or larger than the original.
There are different types of homothecy. The direct dilation occurs when the constant is greater than 0 , so that all the homothetic points are on the same side as compared to the center . The reverse homotecia instead assumed that the constant is smaller than 0 ; in this case, the points are arranged at opposite ends relative to the O point .
Among the properties of homothecy, it should be noted that the center is the only double point (it does not vary). The lines that pass through the center are double, although the points that form it are not, while the lines that do not pass through the point O become parallel lines.