Math Gold Medalist

Lor

2024 AMC 8 

Problem 11

The coordinates of $\triangle ABC$ are $A(5,7)$, $B(11,7)$, and $C(3,y)$, with $y>7$” width=”43″ height=”15″ style=”border-width: 0px; border-style: initial; vertical-align: -3px;”>. The area of <img decoding= is 12. What is the value of $y$?

[asy] draw((3,11)--(11,7)--(5,7)--(3,11)); dot((5,7)); label("$A(5,7)$",(5,7),S); dot((11,7)); label("$B(11,7)$",(11,7),S); dot((3,11)); label("$C(3,y)$",(3,11),NW); [/asy]


$\textbf{(A) }8\qquad\textbf{(B) }9\qquad\textbf{(C) }10\qquad\textbf{(D) }11\qquad \textbf{(E) }12$

Area

Area = (base.height)/2

base=6

height = y-7

.

   Solution