3.50: Curves meet; perpendicular bisector of $AB$

The curves $y=x^{2}+x-1$ and $y=2x^{2}-6x+2$ intersect at the points $A$ and $B$. Show that the mid-point of $AB$ is $(2, 9)$.

Show that $C(12, 7)$ lies on the perpendicular bisector $l$ of $AB$.

Point $D$ on $l$ is such that its distance from $AB$ is twice that of $C$ from $AB$. Find the two possible coordinates of $D$.