Respostas

2013-12-07T13:52:55-02:00
Pontos que as retas se encontram:
r:x-y+1=0
s:2x-y-2=0
t:y=0
r\cap s \left \{ {{r:-x+y-1=0} \atop {s:2x-y-2=0} \right..:\ x=3\ e\ y=4
r\cap t \left \{ {{x-y+1=0} \atop {t:y=0}} \right. .:\ x=-1\ e\ y=0
s\cap t \left \{ {{2x-y-2=0} \atop {y=0}} \right. .:\ x=1\ e\ y=0A(3,4)\\B(-1,0)\\C(1,0)

Área do triângulo ABC

A(3,4)
B(-1,0)
C(1,0)
Area_{\Delta ABC}=\frac{\left|\begin{array}{ccc}3&4&1\\-1&0&1\\1&0&1\end{array}\right|}{2}
=\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

Hugs!

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