Given that the line 2x - y + 4 = 0 cuts the parabola y² = 8x at P, Q. We need to find the midpoint of PQ.

Substituting y = 2x + 4 in the equation of parabola.

⇒ (2x + 4)² = 8x

⇒ 4x² + 16x + 16 = 8x

⇒ 4x² + 8x + 16 = 0

⇒ x² + 2x + 4 = 0

Let x₁, x₂ be the roots. Then, x₁ + x₂ = - 2

Now substituting in the equation of the line we get,

⇒

⇒

⇒ y² - 4y + 16 = 0

Let y₁, y₂ be the roots. Then, y₁ + y₂ = 4

Let us assume P be (x₁, y₁) and Q be (x₂, y₂) and R be the midpoint of PQ.

⇒

⇒

⇒ R = (- 1, 2)

∴The correct option is C