G4.2 On the coordinate plane, the points $A(3,7)$ and $B(8,14)$ are reflected about the line $y=k x+c$, where $k$ and $c$ are constants, their images are $C(5,5)$ and $D(12,10)$ respectively. If $R=\frac{k}{c}$, find the value of $R$.
By the property of reflection, the line $y=k x+c$ is the perpendicular bisector of $A, C$ and $B, D$. That is to say, the mid points of $A, C$ and $B, D$ lies on the line $y=k x+c$ $M=$ mid point of $A, C=(4,6), N=$ mid point of $B, D=(10,12)$
By two points form, $\frac{y-6}{x-4}=\frac{12-6}{10-4}$
$$
y=x+2 \Rightarrow k=1, c=2, R=\frac{1}{2}
$$