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Rectangle by 2 vertices

Source: AMC 10 2006B, Problem 20

February 17, 2006
geometryrectangleanalytic geometrygraphing linesslopevectorAMC

Problem Statement

In rectangle ABCD ABCD, we have A \equal{} (6, \minus{} 22), B \equal{} (2006,178), and D \equal{} (8,y), for some integer y y. What is the area of rectangle ABCD ABCD? <spanclass=′latex−bold′>(A)</span>4000<spanclass=′latex−bold′>(B)</span>4040<spanclass=′latex−bold′>(C)</span>4400<spanclass=′latex−bold′>(D)</span>40,000<spanclass=′latex−bold′>(E)</span>40,400 <span class='latex-bold'>(A) </span> 4000 \qquad <span class='latex-bold'>(B) </span> 4040 \qquad <span class='latex-bold'>(C) </span> 4400 \qquad <span class='latex-bold'>(D) </span> 40,000 \qquad <span class='latex-bold'>(E) </span> 40,400
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