Question

Me ajudem Pessoal estou com duvidas !

Answer 1

Boa noite Iuri!


Solução!


Geometria analítica formula da distância entre dois pontos.



$d(a,b)= \sqrt{( x_{a}- x_{1b})^{2}+(y_{a}-y_{b})^{2}}$



$\sqrt{( 2 \sqrt{3} - 4 \sqrt{3} )^{2}+(y-1)^{2}}=4\\\\\\ \sqrt{( 2 - 4 )\sqrt{3} )^{2}+(y-1)^{2}}=4\\\\\\ \sqrt{( -2 \sqrt{3} )^{2}+(y-1)^{2}}=4\\\\\\ \sqrt{( 4.3 )^{2}+(y^{2}-2y+1 )}=(4)^{2} \\\\\\ 12 +y^{2}-2y+1 =16\\\\\\\ y^{2}-2y+1-16+12=0\\\\\\ y^{2}-2y-3=0$


$a=1\\\\ b=-2\\\\ c=-3\\\\\ y= \dfrac{-b\pm \sqrt{b^{2}-4.a.c } }{2.a} \\\\\\ y=\dfrac{-(-2)\pm \sqrt{(-2)^{2}-4.1.(-3) } }{2.1} \\\\\\ y=\dfrac{2\pm \sqrt{4+12} }{22} \\\\\\ y=\dfrac{2\pm \sqrt{16 } }{2} \\\\\\ y=\dfrac{2\pm 4 }{2} \\\\\\ y_{1}= \dfrac{2+4}{2} = \dfrac{6}{2}=3 \\\\\\\ y_{2}= \dfrac{2-4}{2} = \frac{-2}{2} =-1$


Os dois valores de y são verdadeiro para a distância.


$\boxed{Resposta: y=-1~~y=3}$


Boa noite!

Bons estudos!