The equation of a curve is \(y = x^2 - 4x + 7\) and the equation of a line is \(y + 3x = 9\). The curve and the line intersect at the points \(A\) and \(B\).

1. The midpoint of \(AB\) is \(M\). Show that the coordinates of \(M\) are \(\left( \frac{1}{2}, \frac{7}{2} \right)\).
2. Find the coordinates of the point \(Q\) on the curve at which the tangent is parallel to the line \(y + 3x = 9\).
3. Find the distance \(MQ\).