Consider the parabola x2=16y whose axis is the y-axis. A point Q(4,9) is taken in the plane.
a. (i) Find the coordinates of the point Q′ that is the reflection of Q in the axis of the parabola.
b. (ii) Determine the coordinates of the midpoint M of the segment QQ′.
c. (iii) Show that the midpoint M obtained in part (ii) lies on the axis of the parabola and calculate its distance from the vertex.