MathDB
Classic Triangle Area problem

Source: 2024 AMC 8 P11

January 25, 2024
AMC 82024 AMC 8AMCgeometryanalytic geometry

Problem Statement

The coordinates of ABC\triangle ABC are A(5,7)A(5, 7), B(11,7)B(11, 7), C(3,y)C(3, y), with y>7y > 7. The area of ABC\triangle ABC is 1212. What is the value of yy?
[asy] size(10cm); draw((5,7)--(11,7)--(3,11)--cycle); label("A(5,7)A(5,7)", (5,7),S); label("B(11,7)B(11,7)", (11,7),S); label("C(3,y)C(3,y)", (3,11),W); [/asy]
<spanclass=latexbold>(A)</span>8<spanclass=latexbold>(B)</span>9<spanclass=latexbold>(C)</span>10<spanclass=latexbold>(D)</span>11<spanclass=latexbold>(E)</span>12<span class='latex-bold'>(A) </span> 8\qquad<span class='latex-bold'>(B) </span> 9\qquad<span class='latex-bold'>(C) </span> 10\qquad<span class='latex-bold'>(D) </span> 11\qquad<span class='latex-bold'>(E) </span> 12