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Answer:AStep-by-step explanation:Giveny - 2x - 8 = 0 ( add 2x + 8 to both sides )y = 2x + 8 → (1)y² + 8x = 0 → (2)Substitute y = 2x + 8 into (2)(2x + 8)² + 8x = 0 ← expand left side using FOIL and simplify4x² + 32x + 64 + 8x = 04x² + 40x + 64 = 0 ( divide through by 4 )x² + 10x + 16 = 0 ← in standard form(x + 8)(x + 2) = 0 ← in factored formx + 8 = 0 ⇒ x = - 8x + 2 = 0 ⇒ x = - 2Substitute these values into (1) for corresponding values of yx = - 8 : y = 2(- 8) + 8 = - 16 + 8 = - 8 ⇒ P (- 8, - 8)x = - 2 : y = 2(- 2) + 8 = - 4 + 8 = 4 ⇒ Q (- 2, 4 )Calculate the length of PQ using the distance formulaPQ = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]with (x₁, y₁ ) = P (- 8, - 8) and (x₂, y₂ ) = Q (- 2, 4 )PQ = [tex]\sqrt{(-2-(-8))^2+(4-(-8))^2}[/tex]       = [tex]\sqrt{(-2+8)^2+(4+8)^2}[/tex]        = [tex]\sqrt{6^2+12^2}[/tex]        = [tex]\sqrt{36+144}[/tex]        = [tex]\sqrt{180}[/tex]        = [tex]\sqrt{36(5)}[/tex]        = [tex]\sqrt{36}[/tex] × [tex]\sqrt{5}[/tex]         = 6[tex]\sqrt{5}[/tex] → A