How should I find the four vertices of a rectangle if I have its center of gravity and it length and width?

Question

basically all I want to know is in the question.
I know that in a square if I have the length of it and its center of gravity I can find the vertices by this formula:
If the coordinates of the center of gravity is G(1, 2) and its length is 3, and suppose the four vertices are A, B, C and D:
XA = 1 - 3/2
YA = 2 - 3/2
Etc...

Answer 1

If you have a rectangle $ABCD$ where

$AB$ is parallel to $x-$axis
$|AB| = |CD| = a, |BC| = |AD| = b; a, b \gt 0$
Coordinates of $G (h, k)$

Then the coordinates of vertices are given by $(h \pm \frac{a}{2}, k \pm \frac{b}{2})$. Going anticlockwise starting from $A$, the signs are $(+, +), (-, +), (-, -) $ and $(+, -)$.

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Note that the vertices of the rectangle are on a circle with radius $\frac{\sqrt{a^2+b^2}}{2}$ with center at $G(h, k)$. If we rotate the rectangle by angle $x$ in anticlockwise direction by point $G$, $A'$ is our new $A$ and coordinates of $A'$ is given by,

$\displaystyle \big(h + \frac{a \cos x - b \sin x}{2}, k + \frac{a \sin x + b \cos x}{2}\big)$

Other vertices follow the same pattern.