Resposta :
Pontos que as retas se encontram:
[tex]r:x-y+1=0[/tex]
[tex]s:2x-y-2=0[/tex]
[tex]t:y=0[/tex]
[tex]r\cap s \left \{ {{r:-x+y-1=0} \atop {s:2x-y-2=0} \right..:\ x=3\ e\ y=4[/tex]
[tex]r\cap t \left \{ {{x-y+1=0} \atop {t:y=0}} \right. .:\ x=-1\ e\ y=0[/tex]
[tex]s\cap t \left \{ {{2x-y-2=0} \atop {y=0}} \right. .:\ x=1\ e\ y=0[/tex][tex]A(3,4)\\B(-1,0)\\C(1,0)[/tex]
Área do triângulo ABC
[tex]A(3,4)[/tex]
[tex]B(-1,0)[/tex]
[tex]C(1,0)[/tex]
[tex]Area_{\Delta ABC}=\frac{\left|\begin{array}{ccc}3&4&1\\-1&0&1\\1&0&1\end{array}\right|}{2}[/tex]
[tex]=\frac{\left|\begin{array}{ccc}3& 4&1\\-1& 0&1\\1&0&1\end{array}\right|\left\begin{array}{cc}3&4\\-1&0\\1&0\end{array}\right|}{2}=\frac{0+4+0+4-0-0}{2}=\frac{8}{2}=4[/tex]
Hugs!
[tex]r:x-y+1=0[/tex]
[tex]s:2x-y-2=0[/tex]
[tex]t:y=0[/tex]
[tex]r\cap s \left \{ {{r:-x+y-1=0} \atop {s:2x-y-2=0} \right..:\ x=3\ e\ y=4[/tex]
[tex]r\cap t \left \{ {{x-y+1=0} \atop {t:y=0}} \right. .:\ x=-1\ e\ y=0[/tex]
[tex]s\cap t \left \{ {{2x-y-2=0} \atop {y=0}} \right. .:\ x=1\ e\ y=0[/tex][tex]A(3,4)\\B(-1,0)\\C(1,0)[/tex]
Área do triângulo ABC
[tex]A(3,4)[/tex]
[tex]B(-1,0)[/tex]
[tex]C(1,0)[/tex]
[tex]Area_{\Delta ABC}=\frac{\left|\begin{array}{ccc}3&4&1\\-1&0&1\\1&0&1\end{array}\right|}{2}[/tex]
[tex]=\frac{\left|\begin{array}{ccc}3& 4&1\\-1& 0&1\\1&0&1\end{array}\right|\left\begin{array}{cc}3&4\\-1&0\\1&0\end{array}\right|}{2}=\frac{0+4+0+4-0-0}{2}=\frac{8}{2}=4[/tex]
Hugs!