9747: ABC197 —— D - Opposite
[Creator : ]
Description
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 $y_1$.
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
Input is given from Standard Input in the following format:
```
$N$
$x_0$ $y_0$
$x_{\frac{N}{2}}$ $y_{\frac{N}{2}}$
```
```
$N$
$x_0$ $y_0$
$x_{\frac{N}{2}}$ $y_{\frac{N}{2}}$
```
Output
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 $10^{-5}$.
Your output is considered correct when, for each value printed, the absolute or relative error from our answer is at most $10^{-5}$.
Constraints
- $4 \le N \le 100$
- $N$ is even.
- $0 \le x_0, y_0 \le 100$
- $0 \le x_{\frac{N}{2}}, y_{\frac{N}{2}} \le 100$
- $(x_0, y_0) \neq (x_{\frac{N}{2}}, y_{\frac{N}{2}})$
- All values in input are integers.
- $N$ is even.
- $0 \le x_0, y_0 \le 100$
- $0 \le x_{\frac{N}{2}}, y_{\frac{N}{2}} \le 100$
- $(x_0, y_0) \neq (x_{\frac{N}{2}}, y_{\frac{N}{2}})$
- All values in input are integers.
Sample 1 Input
4
1 1
2 2
Sample 1 Output
2.00000000000 1.00000000000
We are given $p_0=(1,1)$ and $p_2=(2,2)$.
The fact that $p_0,\ p_1,\ p_2,\ p_3$ form a square and they are in counter-clockwise order uniquely determines the coordinates of the other vertices, as follows:
The fact that $p_0,\ p_1,\ p_2,\ p_3$ form a square and they are in counter-clockwise order uniquely determines the coordinates of the other vertices, as follows:
- $p_1=(2,1)$
- $p_3=(1,2)$
Sample 2 Input
6
5 3
7 4
Sample 2 Output
5.93301270189 2.38397459622