The idea of homothecy It is used in the field of geometry to allude to link established by two figures when their corresponding points are aligned in a fixed point. It is, therefore, a correspondence between geometric figures.
Homothecy implies starting from a point permanent known as center or point O. To get the homothetic points, the distances are multiplied by a common factor: thus, at each point P, corresponds to a point P ‘, both aligned with the point O.
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 in other 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 homothecy occurs when the constant is greater than 0, so that all homothetic points are on the same side compared to center. The reverse homothecyinstead, assume that the constant is less than 0; in this case, the points are arranged at opposite ends with respect to the point O.
Between 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 they become parallel lines.