Determining the points of a rotated square.

Question

I have a square with the following four corner points:

(0, 0),(100 0),(100 100),(0, 100).

The square is then rotated clockwise ten degrees.

What is the formula that will allow me to determine its new location?

Thanks.

Answer 1

Move the square so that it's center is the origin $(0, 0)$. This means moving all points with the vector $(-50, -50)$.

As complex numbers, the points would be $p_1=-50+50i$, $p_2=50+50i$, $p_3=50-50i$, $p_4=-50-50i$. These points can be rotated 10°(=$\frac{\pi}{18}rad$) clockwise by multiplying them with $e^{\frac{\pi*i}{18}}$. The points (complex numbers) that you then end up with should be moved back by reversing the movement we did in the first step (move all points (50, 50)).

I have no calculator with support for complex numbers here, so you will have to do the actual calculations yourself.