$D$ is located at $(4,6)$, while $E$ has coordinates $(e,e)$. $F$ is at $(-f,5f)$.
(a)[5]
The length $DE$ is $\sqrt{20}$. Set up an equation in $e$ and solve it to determine the possible coordinates of $E$.
(b(i))[4]
The gradient of the perpendicular bisector of $DF$ is $\frac{3}{2}$. Determine the value of $f$.
(b(ii))[3]
The equation of the perpendicular bisector of $DF$ is $2y = 3x + k$. Determine $k$.
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