How prove this frog can finite steps jump the point $(\frac{1}{5},\frac{1}{17})$ 
A frog starts at $A(0,0)$ and jumps repeatedly, such that jump covers a distance of exactly $1$, and  such each point jumped to has rational coordinates. Show that:
(1): This frog can jump with finitely many jumps to the point $(\frac{1}{5},\frac{1}{17})$
(2): This frog can't jump with finitely many jumps to the point $(0,\dfrac{1}{4})$

I think this problem is interesting. And note
$$1=\left(\frac{3}{5}\right)^2+\left(\frac{4}{5}\right)^2$$
so I want to first jump to $(\frac{3}{5},\frac{4}{5})$, but then I don't know how to continue.


For part (1), observe that 
$$\left(\frac{3}{5},\frac{4}{5}\right) + \left(\frac{3}{5},-\frac{4}{5}\right) + (-1, 0)
+ \left(\frac{15}{17},-\frac{8}{17}\right) + \left(-\frac{15}{17},-\frac{8}{17}\right) 
+ (0, 1)
= \left(\frac{1}{5},\frac{1}{17}\right).$$
