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Geometry Difficulty 4.6 AIME Prove it Ukraine

In the coordinate plane xOyxOy, depict the set of all points such that ∣y−x∣=2−y−x|y - x| = 2 - y - x.

Solution

Вихідне співвідношення рівносильне системі
{y=1,x=1;y≤2−x. \begin{cases} y = 1, \\ x = 1; \\ y \le 2 - x. \end{cases}
Слід зобразити множину точок {(x;1):x≤1}∪{(1;y):y≤1}\{(x; 1) : x \le 1\} \cup \{(1; y) : y \le 1\}.

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