The Hebrew root חצה (chet-tzadi-heh) carries the core idea of dividing, separating, or cutting off.

חצי (chetzi) – half, indicating a division into two equal parts
מחיצה (mechitza) – a partition or divider, often used in a religious context to separate men and women in synagogues
נחצה (nichtsa) – was divided, the passive form of the verb, showing something was split
חוצות (chutzot) – streets or public squares, which divide and organize the urban space
להחצין (lehachzin) – to externalize or express something outwardly, separating it from one’s inner thoughts

The connection between "fence" (חַיִץ – chayitz) and "divide" (חוֹצֶה – chotze) is indeed strong, highlighting how a physical barrier creates separation and defines boundaries. This root also extends to more abstract concepts like differentiating between ideas or taking a middle ground."

and חצה are likely closely related – a fence (chayitz) divides (chotze) and leaves something outside (chutz). From the root חצה, we get such words as – balason

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