Resposta:
[tex]\textsf{Leia abaixo}[/tex]
Explicação passo a passo:
[tex]\begin{cases}\mathsf{x + y = 2}\\\mathsf{(x - 1)^2 + (y - 1)^2 = 8}\end{cases}[/tex]
[tex]\mathsf{x = 2 - y}[/tex]
[tex]\mathsf{(1 - y)^2 + (y - 1)^2 = 8}[/tex]
[tex]\mathsf{(1 - 2y + y^2) + (y^2 - 2y + 1) = 8}[/tex]
[tex]\mathsf{2y^2 - 4y +2 = 8}[/tex]
[tex]\mathsf{y^2 - 2y -3 = 0}[/tex]
[tex]\mathsf{y^2 - 2y -3 + 4 = 4}[/tex]
[tex]\mathsf{y^2 - 2y + 1 = 4}[/tex]
[tex]\mathsf{(y - 1)^2 = 4}[/tex]
[tex]\mathsf{y - 1 = \pm\:2}[/tex]
[tex]\mathsf{y' = 2 + 1 = 3}[/tex]
[tex]\mathsf{y'' = -2 + 1 = -1}[/tex]
[tex]\mathsf{x' = 2 - 3 = -1}[/tex]
[tex]\mathsf{x'' = 2 - (-1) = 2 + 1 = 3}[/tex]
[tex]\mathsf{A(x';y') = A(-1;3)}[/tex]
[tex]\mathsf{B(x'';y'') = B(3;-1)}[/tex]
[tex]\mathsf{d_{AB} = \sqrt{(x_A - x_B)^2 + (y_A - y_B)^2}}[/tex]
[tex]\mathsf{d_{AB} = \sqrt{(-1 - 3)^2 + (3 - (-1))^2}}[/tex]
[tex]\mathsf{d_{AB} = \sqrt{(-1 - 3)^2 + (3 + 1)^2}}[/tex]
[tex]\mathsf{d_{AB} = \sqrt{(-4)^2 + (4)^2}}[/tex]
[tex]\mathsf{d_{AB} = \sqrt{16 + 16}}[/tex]
[tex]\mathsf{d_{AB} = \sqrt{32}}[/tex]
[tex]\mathsf{d_{AB} = \sqrt{2.4^2}}[/tex]
[tex]\boxed{\boxed{\mathsf{d_{AB} = 4\sqrt{2}}}}[/tex]
