<p>Triangle <img alt="$ABC$" height="13" src="https://latex.artofproblemsolving.com/e/2/a/e2a559986ed5a0ffc5654bd367c29dfc92913c36.png" width="42" /> has vertices <img alt="$A = (3,0)$" height="18" src="https://latex.artofproblemsolving.com/9/c/7/9c73ed8e69dbdf7240eb8185bfaf433b614fc6d8.png" width="76" />, <img alt="$B = (0,3)$" height="18" src="https://latex.artofproblemsolving.com/5/3/c/53c39306a7f6400bb8570b0394aaa761b8d0abb3.png" width="77" />, and <img alt="$C$" height="12" src="https://latex.artofproblemsolving.com/c/3/3/c3355896da590fc491a10150a50416687626d7cc.png" width="14" />, where <img alt="$C$" height="12" src="https://latex.artofproblemsolving.com/c/3/3/c3355896da590fc491a10150a50416687626d7cc.png" width="14" /> is on the line <img alt="$x + y = 7$" height="15" src="https://latex.artofproblemsolving.com/3/a/4/3a4101381a47c3b67d875532d1ae8149dc863d69.png" width="75" />. What is the area of <img alt="$\triangle ABC$" height="18" src="https://latex.artofproblemsolving.com/8/c/3/8c3a2d2224f7d163b46d702132425d47828bf538.png" width="61" />?</p>

Question No: 293

Triangle $ABC$ has vertices $A = (3,0)$ , $B = (0,3)$ , and $C$ , where $C$ is on the line $x + y = 7$ . What is the area of $\triangle ABC$ ?

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Tags: Algebra Geometry Probability

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