Score : $400$ points
On a two-dimensional coordinate plane where the $\mathrm{x}$ axis points to the right and the $\mathrm{y}$ axis points up, we have a regular $N$-gon with $N$ vertices $p_0, p_1, p_2, \dots, p_{N - 1}$.
Here, $N$ is guaranteed to be even, and the vertices $p_0, p_1, p_2, \dots, p_{N - 1}$ are in counter-clockwise order.
Let $(x_i, y_i)$ denotes the coordinates of $p_i$.
Given $x_0$, $y_0$, $x_{\frac{N}{2}}$, and $y_{\frac{N}{2}}$, find $x_1$ and $y_1$.
Input is given from Standard Input in the following format:
$N$
$x_0$ $y_0$
$x_{\frac{N}{2}}$ $y_{\frac{N}{2}}$
Print $x_1$ and $y_1$ in this order, with a space in between.
Your output is considered correct when, for each value printed, the absolute or relative error from our answer is at most $10^{-5}$.
4 1 1 2 2
2.00000000000 1.00000000000
We are given $p_0 = (1, 1)$ and $p_2 = (2, 2)$.
The fact that $p_0$, $p_1$, $p_2$, and $p_3$ form a square and they are in counter-clockwise order uniquely determines the coordinates of the other vertices, as follows:
6 5 3 7 4
5.93301270189 2.38397459622