MathDB
What's that region?

Source: 2017 AMC 10A #12, 12A #9

February 8, 2017
AMCAMC 12AMC 12 A2017 AMC 12AAMC 102017 AMC 10ASets

Problem Statement

Let SS be the set of points (x,y)(x,y) in the coordinate plane such that two of the three quantities 33, x+2x+2, and y4y-4 are equal and the third of the three quantities is no greater than this common value. Which of the following is a correct description of SS?
<spanclass=latexbold>(A)</span>a single point<spanclass=latexbold>(B)</span>two intersecting lines<spanclass=latexbold>(C)</span>three lines whose pairwise intersections are three distinct points<spanclass=latexbold>(D)</span>a triangle<spanclass=latexbold>(E)</span>three rays with a common endpoint<span class='latex-bold'>(A) </span> \text{a single point} \qquad <span class='latex-bold'>(B) </span> \text{two intersecting lines} \\ \\ <span class='latex-bold'>(C) </span> \text{three lines whose pairwise intersections are three distinct points} \\ \\ <span class='latex-bold'>(D) </span> \text{a triangle} \qquad <span class='latex-bold'>(E) </span> \text{three rays with a common endpoint}