Question

Determine a área do triângulo cujos vértices são os pontos de intersecção das retas de equações x-y+1=0, 2x-y-2=0 e y=0.
Obrigadaaa a quem puder me ajudar!! =)

Answer 1

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=0$$A(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!