Question

a distância do ponto A(x,1)ao ponto B(0,2) e igual a 3, calcule A

Answer 1

Fórmula distância entre dois pontos

$D= \sqrt{ ( x_{2}- x_{1} ) ^{2}+( y_{2} - y_{1} )^2 }$

$\sqrt{(0-x)^2+(2-1)^2} =3 \\ \\ \sqrt{(-x)2+1^2} =3 \\ \\ \sqrt{ x^{2} +1} =3 \\ \\ ( \sqrt{(x^2+1)} )^2=3^2 \\ \\ x^{2} +1=9 \\ \\ x^2=9-1 \\ \\ x^2=8 \\ \\ x=+- \sqrt{8} \\ \\ x= +- 2 \sqrt{2}$

$A(2 \sqrt{2} ,1) \\ \\ A(-2 \sqrt{2},1)$

Answer 2

$A(x,1)\ ;\ B(0,2)\ ;\ D_{AB}=3\\\\\\ D_{AB}= \sqrt{(x_B-x_A)^2+(y_B-y_A)^2} \\\\\\ 3= \sqrt{(0-x)^2+(2-1)^2} \to \\\\ 3= \sqrt{0-0x-0x+x^2+(1)^2} \to \\\\ 3= \sqrt{x^2+1} \to \\\\ (3)^2= (\sqrt{x^2+1})^2 \to \\\\ 9=x^2+1\to \\\\9-1=x^2\to\\\\ x^2=8\to \\\\x= \sqrt{8} \to\\\\ x= 2\sqrt{2}$