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 homothecy**instead, 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.