3.37: Line meets curve; point on perpendicular bisector

The line $y=3x-2$ intersects the curve $x^{2}-xy+y^{2}=2$ at $A$ and $B$. The point $C\!\left(k,\dfrac{8}{7}\right)$ lies on the perpendicular bisector of $AB$. Find the exact value of $k$.

The point $D$ lies on the perpendicular bisector of $AB$ such that $D$ is the reflection of $C$ in the line $AB$. Find the coordinates of $D$.