MathDB
Boundary of set S

Source: 1978 AHSME Problem 25

June 18, 2014
analytic geometryAMC

Problem Statement

Let uu be a positive number. Consider the set SS of all points whose rectangular coordinates (x,y)(x, y ) satisfy all of the following conditions:
(i) a2≤x≤2a(ii) a2≤y≤2a(iii) x+y≥a(iv) x+a≥y(v) y+a≥x\text{(i) }\frac{a}{2}\le x\le 2a\qquad\text{(ii) }\frac{a}{2}\le y\le 2a\qquad\text{(iii) }x+y\ge a \\ \\ \qquad\text{(iv) }x+a\ge y\qquad \text{(v) }y+a\ge x
The boundary of set SS is a polygon with
<spanclass=′latex−bold′>(A)</span>3 sides<spanclass=′latex−bold′>(B)</span>4 sides<spanclass=′latex−bold′>(C)</span>5 sides<spanclass=′latex−bold′>(D)</span>6 sides<spanclass=′latex−bold′>(E)</span>7 sides<span class='latex-bold'>(A) </span>3\text{ sides}\qquad<span class='latex-bold'>(B) </span>4\text{ sides}\qquad<span class='latex-bold'>(C) </span>5\text{ sides}\qquad<span class='latex-bold'>(D) </span>6\text{ sides}\qquad <span class='latex-bold'>(E) </span>7\text{ sides}
Back to ProblemsView on AoPS