5 The equation of a curve is \(y = x ^ { 2 } - 4 x + 7\) and the equation of a line is \(y + 3 x = 9\). The curve and the line intersect at the points \(A\) and \(B\).
- The mid-point of \(A B\) is \(M\). Show that the coordinates of \(M\) are \(\left( \frac { 1 } { 2 } , 7 \frac { 1 } { 2 } \right)\).
- Find the coordinates of the point \(Q\) on the curve at which the tangent is parallel to the line \(y + 3 x = 9\).
- Find the distance \(M Q\).