To find the points of intersection, set the equations equal: \(x^2 - 4x + 4 = x\).

Rearrange to form a quadratic equation: \(x^2 - 5x + 4 = 0\).

Factor the quadratic: \((x - 1)(x - 4) = 0\).

Thus, \(x = 1\) and \(x = 4\).

Substitute back to find \(y\) coordinates: \(y = 1\) when \(x = 1\) and \(y = 4\) when \(x = 4\).

Points \(A\) and \(B\) are \((1, 1)\) and \((4, 4)\).

The midpoint of \(AB\) is \(\left( \frac{1 + 4}{2}, \frac{1 + 4}{2} \right) = \left( \frac{5}{2}, \frac{5}{2} \right)\).