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Ukrainian Mathematical Olympiad

Geometry Difficulty 4.6 AIME Prove it Ukraine

In the coordinate plane $xOy$ , depict the set of all points such that $|y - x| = 2 - y - x$ .

Solution

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

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