center of gravity given four weights

Question

I have this problem. I have four points that corresponds to four vertices of rectangle. Every vertex has a load cell that return a weight. How can I calculate the center of gravity, in a range of 0-100?

Any idea? Thanks

--- EDIT ----

Look the image:

Answer 1

Let the origin be one corner of the rectangle and the $x$ axis along the length $L$. If the width is $W$ you have measurements at $(0,0),(L,0),(0,W),(L,W)$. If $w(x,y)$ is the weight measured at $x,y$ you have the $x$ position of the CG is $$x_{CG}=\frac {w(L,0)+w(L,W)}{w(L,0)+w(L,W)+w(0,W+w(0,0)}L$$ If you want a value in $[0,100]$ you probably mean the percentage of the length, so divide this by the length and express it in percent. Do the same in the other axis.

Answer 2

Let's assume your centre of gravity is at point $P(x,y)$

Let's calculate the $x$ coordinate of the gravity centre.

$$x=\frac{10*0+20*0+0*0+5*L}{10+20+0+5}=\frac{5L}{35}=\frac{L}{7}$$ $$y=\frac{10*0+20*L+0*W+5*W}{35}=\frac{4L+W}{7}$$