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Source: AMC10B 2017 #8

February 16, 2017
AMCAMC 10AMC 10 Banalytic geometry2017 AMC 10B

Problem Statement

Points A(11,9)A(11,9) and B(2,3)B(2,-3) are vertices of ABC\triangle ABC with AB=ACAB=AC. The altitude from AA meets the opposite side at D(1,3)D(-1, 3). What are the coordinates of point CC?
<spanclass=latexbold>(A)</span>(8,9)<spanclass=latexbold>(B)</span>(4,8)<spanclass=latexbold>(C)</span>(4,9)<spanclass=latexbold>(D)</span>(2,3)<spanclass=latexbold>(E)</span>(1,0)<span class='latex-bold'>(A) </span> (-8, 9)\qquad <span class='latex-bold'>(B) </span> (-4, 8)\qquad <span class='latex-bold'>(C) </span> (-4,9)\qquad <span class='latex-bold'>(D) </span> (-2, 3)\qquad <span class='latex-bold'>(E) </span> (-1, 0)